Bibliography

From DispersiveWiki

Important note

This bibliography was ported over from the previous incarnation of these pages. It should now be considered obsolete. Instead, we are now giving each reference its own page.

The naming system for these articles was somewhat implicit and ad hoc; we are currently forming more explicit standards for this.

References

Aa2002

M. Aassilla, Nonexistence de solutions globales de certains equations d'ondes nonlineaires, C. R. Acad. Sci. Paris. 334 (2002), 961-966.

AbdBnFelSau1989

L. Abdelouhab, J. Bona, M. Felland, J. Saut, Nonlocal models for nonlinear dispersive waves, Phys. D 40 (1989), 360-392.

AbKauNeSe1974

M. Ablowitz, D. Kaup, A. Newell, H. Segur, The inverse scattering transform-Fourier analysis for nonlinear problems, Studies in Appl. Math. 53 (1974), no. 4, 249-315.

AbFs1983

M. Ablowitz, A. Fokas, The inverse scattering transform for the Benjamin-Ono equation, a pivot for multidimensional problems, Stud. Appl. Math. 68 (1983), 1-10.

AbHab1975

M. Ablowitz, R. Haberman, Nonlinear evolution equations in two and three dimensions, Phys. Rev. Lett. 35 (1975), 1185-1188.

AbMa1981

M. Ablowitz, Y. Ma, The periodic nonlinear Schrodinger equation, Stud. Appl. Math. 65 (1981), 113-158.

AbSe1977

M. Ablowitz, H. Segur, Asymptotic solutions of the Korteweg de Vries equation, Stud. Appl. Math. 57 (1977), 13-44.

AdhAds1988

H. Added, S. Added, Equations of Langmuir turbulence and non-linear Schrodinger equation: Smoothness and approximations, JFA 79 (1988), 183-210.

AgYok1998

R. Agemi, K. Yokoyama, The null condition and global existence of solutions to systems of wave equations with different speeds, Adv. Nonlinear PDE and Stochastics (1998), 43-86.

AxPgSac1997

J.C. Alexander, R.L. Pego, R.L. Sachs, On the transverse instability of solitary waves in the Kadomtsev-Petviashvili equation, Phys. Lett. A. 226 (1997), 187-192.

Al1995

S. Alinhac, Blowup for nonlinear hyperbolic equations, Boston: Birkhauser, 1995, Progress in Nonlinear DE and their Applications, 17.

Al1999

S. Alinhac, Blow up of small data solutions for a class of quasilinear wave equations in two space dimensions I, Annals of Mathematics 149 (1999), 97-127.

Al1999b

S. Alinhac, Blow up of small data solutions for a class of quasilinear wave equations in two space dimensions II, Acta Math. 182 (1999), 1-23.

Al2000

S. Alinhac, Rank 2 singular solutions for quasilinear wave equations, IMRN 18 (2000), 955-984.

Al2001

S. Alinhac, The null condition for quasilinear wave equations in two space dimensions I, Invent. Math. 145 (2001), 597-618.

Al2001b

S. Alinhac, The null condition for quasilinear wave equations in two space dimensions II, AJM 123 (2001), 1071-1101.

Al2003

S. Alinhac, An example of blowup at infinity for a quasilinear wave equation, Asterisque 284 (2003), 1-91.

AcIb2000

S. Anco, J. Isenberg, Global existence for wave maps with torsion, CPDE 25 (2000), 1669-1702.

AnMc-p

L. Andersson, V. Moncrief, Elliptic-Hyperbolic systems and the Einstein equations, preprint.

Ant2003

C. Antonini, Lower bounds for the L^2 minimal periodic blowup solutions of critical nonlinear Schrodinger equation, DIE 15 (2002), 749-768.

AntMe2001

C. Antonini, F. Merle, Optimal bounds on positive blowup solutions for a semilinear wave equation, IMRN 21 (2001), 1143-1167.

ArYa2000

G. Artbazar, K. Yajima, The L^p continuity of wave operators for one dimensional Schrodinger operators, J. Math. Sci. Univ. Tokyo 7 (2000), 221-240.

AsCoeWgg1996

J. M. Ash, J. Cohen, G. Wang, On strongly interacting internal solitary waves, J. Fourier Anal. Appl., 2 (1996), 507-517.

Bch1984

A. Bachelot, Probleme de Cauchy pour des systemes hyperboliques semilineaires, Ann. IHP (Anal. nonlin), 1 (1984), 453-478.

BchNic1993

A. Bachelot, J-P. Nicolas, Equation non-lineaire de Klein-Gordon dans des metriquesde type Schwarzchild, C.R. Acad. Sci. Paris. 316 (1993), 1047-1050

BlChd1978

J. B. Baillon, J. M. Chadam, The Cauchy problem for the coupled Schrodinger-Klein-Gordon equations, in "Contemporary Developments in Continuum Mechanics and Partial Differential Equations", G. M. de La Penha and L. A. Medeiros eds., North Holland, Amsterdam 1978

BaeSgZz1990

J. Baez, I. Sega, Z. Zhou, The global Goursat problem and scattering for nonlinear wave equations, J. Funct. Anal. 93 (1990), 239-269.

BaCh1999

H. Bahouri, J-Y. Chemin, Équations d'ondes quasilinéaires et les inegalites de Strichartz, Amer. J. Math.121 (1999), 1337-1377.

BaCh1999b

H. Bahouri, J-Y. Chemin, Équations d'ondes quasilinéaires et effet dispersif, IMRN 21 (1999), 1141-1178.

BaCh2002

H. Bahouri, J-Y. Chemin, Quasilinear Wave equations and Microlocal Analysis, ICM 2002, Vol III, 141-154.

BaCh-p

H. Bahouri, J-Y. Chemin, Microlocal analysis, bilinear estimates, and cubic quasilinear wave equation, preprint.

BaGd1997

H. Bahouri and P.Gerard, High frequency approximation of solutions to critical nonlinear wave equations, Prepublications 97-34, Universite de Paris-Sud, Mai 1997. Appeared in: Amer. J. Math 121 (1999), 131-175.

BaGdXu2000

H. Bahouri, P. Gerard, C. Xu, Espaces de Besov et estimations de Strichartz generalisees sur le groupe de Heisenberg, Journal d'Analyse Mathematique 82 (2000), 93-118.

BaSa1998

H. Bahouri and J.Shatah, Decay estimates for the critical semilinear wave equation, Ann. Inst. H. Poincare Anal. Non Lineaire 15 (1998), no. 6, 783-789.

Ban-p

V. Banica, On the nonlinear Schrodinger dynamics on S^2, preprint.

Ban-p2

V. Banica, Dispersion and Strichartz inequalities for Schrodinger equations with singular coefficients, preprint.

Ban-p3

V. Banica, Remarks on the blowup for the nonlinear Schrodinger equation with critical mass on a plane domain, preprint.

Bb1984

J.E. Barab, Nonexistence of asymptotically free solutions for a nonlinear Schrodinger equation, J. Math. Phys. 25 (1984), 3270-3273.

Be1983

M. Beals, Self-Spreading and strength of Singularities for solutions to semilinear wave equations, Annals of Math 118 (1983), 187-214

BeBz1996

M. Beals, M. Bezard, Low regularity local solutions for field equations, Comm. Partial Differential Equations21 (1996), 79-124.

BecMauSb-p

P. Bechouce, N. Mauser, S. Selberg, Nonrelativistic limit of Klein-Gordon-Maxwell to Schrodinger Poisson, preprint

BecMauSb-p2

P. Bechouce, N. Mauser, S. Selberg, On the asymptotic analysis of the Dirac-Maxwell system in the nonrelativistic limit, preprint

BkOgPo1996

D. Bekiranov, T. Ogawa, G. Ponce, On the well-posedness of Benney's interaction equation of short and long waves, Adv. Diff. Eq. 1 (1996), 919-937.

BkOgPo1997

D. Bekiranov, T. Ogawa, G. Ponce, Weak solvability and well-posedness of the coupled Schrodinger Korteweg-de Vries equation in the capillary-gravity interaction waves, Proc. Amer. Math. Soc. 125 (1997), 2907-2919.

BkOgPo1998

D. Bekiranov, T. Ogawa, G. Ponce, Interaction equations for short and long dispersive waves, J. Funct. Anal. 158 (1998), 357-388.

BcKkZz1999

E. Belchev, M. Kepka, Z. Zhou, Global existence of solutions to nonlinear wave equations, CPDE 24 (1999), 2297-2331.

BcKkZz2002

E. Belchev, M. Kepka, Z. Zhou, Finite time blowup of solutions to semilinear wave equations, JFA 190 (2002), 233-254.

Bj1967

T. Benjamin, Internal waves of permanent form in fluids of great depth, J. Fluid Mech. 29 (1967), 559-562.

Bj1972

T. Benjamin, The stability of solitary waves, Proc. R. Soc. Lond. A. 328 (1972), 153-183.

BjBnMah1972

T. Benjamin, J. Bona, J. Mahony, Model equations for long waves in nonlinear dispersive systems, Phil. Trans. R. Soc. London A 272 (1972), 47-78.

BenKl1992

M. Ben-Artzi, S. Klainerman, Decay and regularity for the Schrodinger equation, J. Anal. Math. 58 (1992), 25-37.

BenSau1999

M. Ben-Artzi, J.C. Saut, Uniform decay estimates for a class of oscillatory integrals and applications, Diff. Int. Eq. 12 (1999), 137-145.

BenKocSau2003

M. Ben-Artzi, H. Koch, J.C. Saut, Dispersion estimates for third order equations in two dimensions, CPDE 28 (2003), 1943-1974.

ByNe1967

D.J. Benney, A.C. Newell, The propagation of nonlinear wave envelopes, J. Math. and Phys. 46 (1967), 133-139.

BerCa1981

H. Berestycki, T. Cazenave, Instabilité des états stationnaires dans les équations de Schrödinger et de Klein-Gordon non linéaires, C. R. Acad. Sc. Paris, t. 293 (1981), 489-492.

BgCcMc1995

B.K. Berger, P. T. Chrusciel, V. Moncrief, On "asymptotically flat" spacetimes with G_2 invariant Cauchy surfaces, Ann. Physics 237 (1995), 322-354.

BiLi-p

H. Biagioni, F. Linares, Ill-posedness for the Derivative Schrodinger and Generalized Benjamin-Ono equations, preprint.

BirPoVe-p

B. Birnir, G. Ponce, L. Vega, On the ill-posedness for the initial value problem for the modified Korteweg-de Vries equation, preprint.

BirKnPoSvVe1996

B. Birnir, C. Kenig, G. Ponce, N. Svanstedt, L. Vega, On the ill-posedness of the IVP for the generalized Korteweg-de Vries and nonlinear Schrödinger equations. J. London Math. Soc. (2) 53 (1996), 551-559.

Biz2000

P. Bizon, Equivariant self-similar wave maps from Minkowski spacetime into 3-sphere. Comm. Math. Phys. 215 (2000), 45-56.

Biz-p

P. Bizon, Formation of singularities in Yang-Mills equations, preprint

BizCjTb2001

P. Bizon, T. Chmaj, Z. Tabor, Formation of singularities for equivariant 2+1 dimensional wave maps into two-sphere, Nonlinearity 14 (2001), no. 5, 1041-1053.

BizOvSi-p

P. Bizon, Y. Ovchinnikov, I. Sigal, Collapse of an Instanton, preprint.

BizTb2001

P. Bizon, Z. Tabor, On blowup for Yang-Mills fields, Phys. Rev. D (3) 64 (2001), 121701.

BluSf2003

P. Blue, A. Soffer, Semilinear wave equations on the Schwarzschild manifold I.Local decay estimates, Adv. Diff Eq. 8 (2003), 595-614.

Bn1975

J. Bona, On the stability theory of solitary waves, Proc. R. Soc. Lond. A. 344 (1975), 363-374.

BnDgKar1986

J. Bona, V.A. Dougalis, O.A. Karakashian, Fully discrete Galerkin methods for the Korteweg-de Vries equation, Comput. Math. Appl. Ser. A 12 (1986), 859-884.

BnLiu2002

J. Bona, Y. Liu, Instability of solitary-wave solutions of the Kadomtsev-Petviashvili equation in three dimensions, ADE 7 (2002), 1-33.

BnPoSauTm1992

J. Bona, G. Ponce, J-C. Saut, M. Tom, A model system for strong interaction between internal solitary waves, CMP 143 (1992), 287-313.

BnSco1976

J. Bona, R. Scott, Solutions of the Korteweg-de Vries equation, in fractional order Sobolev spaces, Duke Math J. 43 (1976), 87-99.

BnSmr1975

J. Bona, R. Smith, The initial-value problem for the Korteweg-de Vries equation, Philos. Trans. Royal Soc. London Series A 278 (1975), 555-601.

BnSouSr1987

J. Bona, P.E. Sougandis, W. Strauss, Stability and instability of solitary waves of Korteweg-de Vries type, Proc. R. Soc. Lond. 411 (1987), 395-412.

BnSuZh-p

J. Bona, S. Sun, B-Y. Zhang, A non-homogeneous boundary-value problem for the Korteweg-de Vries Equation in a Quarter Plane, preprint

BnWi1983

J. Bona, R. Winther, The Korteweg-de Vries equation, posed in a quarter plane, SIAM J. Math. Anal. 14 (1983), 1056-1106.

BnWe-p

J. Bona, F. B. Weissler, Similarity solutions of the generalized Korteweg-de Vries equations, preprint.

Bd1993

A. de Bouard, Analytic solutions to nonelliptic nonlinear Schrodinger equations, JDE 104 (1993), 196-213.

BdDbTs1999

A. de Bouard, A. Debussche, Y. Tsutsumi, White noise driven Korteweg-de Vries equation. J. Funct. Anal. 169 (1999), no. 2, 532-558

BdSau1997

A. de Bouard, J.C. Saut, Solitary waves of generalized Kadomtsev-Petviashvili equations, Annales IHP, Analyse non-lineaire 14 (1997) 211-236.

BdHaSau1997

A. de Bouard, N. Hayashi, J.C. Saut, Global existence of small solutions to a nonlinear relativistic Schrodinger equation, CMP 189 (1997), 73-105.

BdMt2004

A. de Bouard, Y. Martel, Nonexistence of L^2-compact solutions of the Kadomptsev-Petviashvili II equation, Math. Ann. 328 (2004), 525\u2014554.

BctGolPal-p

F. Bouchut, F. Golse, C. Pallard, On classical solutions to the 3D relativistic Vlasov-Maxwell system: Glassey-Strauss's theorem revisited, preprint.

Bo1992

J. Bourgain, A remark on Schrodinger operators, Israel J. Math. 77 (1992), 1-16.

Bo1993

J. Bourgain, Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations I. Schrodinger equations, Geom. Funct. Anal. 3 (1993) 107-156.

Bo1993b

J. Bourgain, Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations II. The periodic KdV equation, Geom. Funct. Anal. 3 (1993) 209-262.

Bo1993c

J. Bourgain, On the Cauchy problem for the Kadomtsev-Petviashvili equation, Geom. Funct. Anal. 3 (1993) 315-341.

Bo1993d

J. Bourgain, Exponential sums and nonlinear Schrodinger equations, Geom. Funct. Anal. 3 (1993) 157-178.

Bo1994

J. Bourgain, On the Cauchy and invariant measure problem for the periodic Zakharov system, Duke Math. J. 76 (1994), 175-202.

Bo1994b

J. Bourgain, Harmonic analysis and nonlinear partial differential equations, Proceedings of the ICM 1994, 31-44, Birkhauser Basel, 1995.

Bo1994c

J. Bourgain, Periodic nonlinear Schrodinger equation and invariant measures, CMP 166 (1994), 1-26.

Bo1995

J. Bourgain, Estimates for cone multipliers, Operator Theory: Advances and Applications, 77 (1995), 41-60.

Bo1995b

J. Bourgain, Aspects of longtime behaviour of solutions of nonlinear Hamiltonian evolution equations, GAFA 5 (1995), 105-140.

Bo1995c

J. Bourgain, Periodic nonlinear Schrodinger equations and invariant measures, CMP 166 (1995), 1-26.

Bo1996

J. Bourgain, On well-posedness of the Zakharov system, Int. Math. Research Notices 11 (1996), 515-546.

Bo1996b

J. Bourgain, Invariant measures for the 2d-defocussing nonlinear Schrodinger equation, Comm. Math. Phys. 176 (1996), 421-445.

Bo1996c

J. Bourgain, On the growth in time of higher order Sobolev norms of smooth solutions of Hamiltonian PDE, IMRN 6 (1996), 277-304.

• kdv_measures.pdf Bo1997 J. Bourgain, [kdv_measures.pdf Periodic Korteweg de Vries equation with measures as initial data], Selecta Math. (N.S.) 3 (1997), 115-159.

Bo1997b

J. Bourgain, On the compactness of support of solutions of dispersive equations, Int. Math. Research Notices 9 (1997), 437-447.

Bo1998

J. Bourgain, Refinements of Strichartz' inequality and applications to 2D-NLS with critical non-linearity, Int. Math. Research Notices, 5 (1998), 253-283.

Bo1998b

J. Bourgain, Scattering in the energy space and below for 3D NLS, J. Anal. Math. 75 (1998), 267-297.

=====Bo1999===== J. Bourgain, New global well-posedness results for non-linear Schrodinger equations, AMS 1999.

Bo1999b

J. Bourgain, Global well-posedness of defocussing 3D critical NLS in the radial case, J. Amer. Math. Soc. 12 (1999), 145-171.

Bo-p

J. Bourgain, Remarks on stability and diffusion in high-dimensional Hamiltonian systems and PDE, preprint.

Bo-p2

J. Bourgain, A remark on normal forms and the I-method for periodic NLS, preprint.

Bo-p3

J. Bourgain, On the Cauchy problem for periodic KdV type equations, preprint.

BoCo1996

J. Bourgain, J. Colliander, On the well-posedness of the Zakharov system, IMRN 11 (1996), 515-546.

BoWg1997

J. Bourgain, W. Wang, Construction of blowup solutions for the nonlinear Schrodinger equation with critical non-linearity, Dedicated to Ennio De Giorgi. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 25 (1997), no. 1-2, 197-215.

Bou1996

N. Bournaveas, Local existence for the Maxwell-Dirac equations in three space dimensions. Comm. Partial Differential Equations 21 (1996) 693-720.

Bou1999

N. Bournaveas, Local existence of energy class solutions for the Dirac-Klein-Gordon equations. Comm. Partial Differential Equations 24 (1999), 1167-1193.

Bou2000

N. Bournaveas, A new proof of global existence for the Dirac Klein-Gordon equations in one space dimension. J. Funct. Anal. 173 (2000), 203-213.

Bou2001

N. Bournaveas, Low regularity solutions of the Dirac Klein-Gordon equations in two space dimensions. Comm. Partial Differential Equations 26 (2001), 1345-1366.

BdmFsShp-p

A. Boutet de Monvel, A. Fokas, The mKdV equation on a half-line, preprint.

BdmShp-p

A. Boutet de Monvel, D. Shepelsky, The mKdV equation on an interval, preprint.

BrlForMai1994

P. Breitenlohner, P. Forgacs, D. Maison, Static spherically symmetric solutions of the Einstein-Yang-Mills equations. Comm. Math. Phys. 163 (1994), no. 1, 141-172.

Br1975

P. Brenner, On L^p - L^{p'} estimates for the wave equation, Math Z. 145 (1975) 251-254.

Br1984

P. Brenner, On spacetime means and everywhere defined scattering operators, Math. Z. 186 (1984), 383-391.

Br1985

P. Brenner, On scattering and everywhere defined scattering operators for nonlinear Klein-Gordon equations, JDE 56 (1985), 310-344.

BrKum2000

P. Brenner, P. Kumlin, On wave equations with supercritical nonlinearities, Arch. Math. 74 (2000), 129-147.

BrzGa1980

H. Brezis, T. Gallouet, Nonlinear Schrodinger evolution equations, Nonlinear Analysis Theory, Methods, and Applications 4 (1980), 677-681.

Bs1967

A.R. Brodsky, On the asymptotic behaviour of solutions of the wave equation, Proc. Amer. Math. Soc. 18 (1967), 207-208.

BroJer2000

J. Bronski, R. Jerrard, Soliton dynamics in a potential, Math Res. Lett. 7 (2000), 329-342.

Bu.1992 C. Bu, On the Well-Posedness of the forced nonlinear Schrodinger Equation, Appl. Anal. 46 (1992), 219-239.

Bu.2000 C. Bu, Nonlinear Schrodinger Equation on the Semi-infinite Line, Chinese J. Contem. Math. 21 (2000), 209-222

Bu.Sr2001 C. Bu, W. Strauss, An inhomogeneous Boundary Value Problem for Nonlinear Schrodinger Equations, JDE 173 (2001), 79-91.

Bub1980

B. Bubnov, On the Cauchy problem for the Korteweg de Vries equation, Soviet Math. Dokl. 21 (1980), 502-505.

Bu1998

N. Burq, Decroissance de l'energie locale de l'equation des ondes pour les probleme exterieur et absece de resonance au voisinage du reel, Acta Math. 180 (1998), 1-29.

Bu1993

N. Burq, Controle l'equation des plaques en presence d'obstacles strictement convexes, Memorie de la SMF 55 (1993), Suppl. au Belletin de la Societe Mathematique de France.

Bu-p

N. Burq, Global Strichartz estimates for nontrapping geometries: A remark about an article by H. Smith and C. Sogge, preprint.

Bu-p2

N. Burq, Smoothing effect for Schrodinger boundary value problems, preprint.

Bu-p3

N. Burq, Estimations de Strichartz pour des perturbations a longe portee de l\u2019operateur de Schrodinger, preprint.

BuGdTz-p

N. Burq, P. Gerard, N. Tzvetkov, Two singular dynamics of the nonlinear Schrodinger equation on a plane domain, preprint.

BuGdTz2002

N. Burq, P. Gerard, N. Tzvetkov, An instability property of the nonlinear Schrodinger equation on S^d, MRL 9 (2002), 323-335.

BuGdTz-p3

N. Burq, P. Gerard, N. Tzvetkov, Strichartz inequalities and the nonlinear Schrodinger equation on compact manifolds, preprint.

BuGdTz-p4

N. Burq, P. Gerard, N. Tzvetkov, On nonlinear Schrodinger equations in exterior domains, preprint.

BuGdTz2003

N. Burq, P. Gerard, N. Tzvetkov, The Cauchy problem for the nonlinear Schrodinger equation on a compact manifold, Proc. Oresund Symposium on PDE, Lund, May 2002, J. Nonlinear Math. Phys. 10 suppl 1. (2003), 1-16.

BuGdTz-p6

N. Burq, P. Gerard, N. Tzvetkov, An example of singular dynamics for the nonlinear Schrodinger equation on bounded domains, Proc. conference on hyperbolic PDE and related topics, Cortona September 2002, preprint.</font></font>

BuGdTz-p7

N. Burq, P. Gerard, N. Tzvetkov, Bilinear Eigenfunction Estimates and the Nonlinear Schroedinger Equation on Surfaces, preprint.</font></font>

BuPlStaTv-p

N. Burq, F. Planchon, J. Stalker, A. Shadi Tahvidar-Zadeh, Strichartz estimates for the Wave and Schrodinger Equations with the Inverse-Square Potential, preprint.

BuPlStaTv-p2

N. Burq, F. Planchon, J. Stalker, A. Shadi Tahvidar-Zadeh, Strichartz estimates for the Wave and Schrodinger Equations with potentials of critical decay, preprint.

BusPer1993

V. Buslaev, G. Perelman, Scattering for the nonlinear Schrodinger equations: states close to a solitary wave, St. Petersburg Math J. 4 (1993), 1111-1142.

BusPer1995

V. Buslaev, G. Perelman, On the stability of solitary waves for nonlinear Schrodinger equations.Nonlinear evolution equations 75-98, Amer. Math. Soc. Transl. Ser. 2, 164, Amer. Math. Soc. Providence, RI 1995.

BusSuc2003

V. Buslaev, C. Sulem, On asymptotic stability of solitary waves for nonlinear Schrodinger equations, Ann. Inst. H. Poincare Anal. Nonlineaire 20 (2003) 3, 419-475.

CafFri1986

L.A. Caffarelli, A. Friedman, the blowup boundary for nonlinearwave equations, TAMS 297 (1986), 223-241.

Cal-p

S. Calogero, Global small solutions of the Vlasov-Maxwell system in absence of incoming radiation., preprint

Car2001

R. Carles, Geometric optics and long-range scattering for one-dimensional nonlinear Schrodinger equations, Comm. Math. Phys. 220 (2001), 41-67.

Car2002

R. Carles, Critical nonlinear Schrodinger equations with and without harmonic potential, Math. Mod. Meth. Appl Sci. 12 (2002), 1513-1523..

Car2002b

R. Carles, Remarks on nonlinear Schrodinger equations with harmonic potential, Ann. Henri Poincare 3 (2002), 757-772.

Car2002c

R. Carles, Critical nonlinear Schrödinger equations with and without harmonic potential, Math. Mod. Meth. Appl. Sci. (M3AS) 12 (2002), 1513-1523

Car2003

R. Carles, Annales IHP, Analyse nonlineaire, 20 (2003) 501-542.

Car-p

R. Carles, Nonlinear Schrodinger equations with repulsive harmonic potential and applications, preprint.

CarFerGal-p

R. Carles, C. Fermanian, I. Gallagher, On the role of quadratic oscillations in nonlinear Schrodinger equations, preprint.

CarKer-p

R. Carles, S. Keraani, On the role of quadratic oscillations in nonlinear Schroedinger equations II. The $L^2$-critical case, preprint.

CarNky-p

R. Carles, Y. Nakamura, Nonlinear Schrodinger equations with Stark potential, preprint.

CarMil-p

R. Carles, Semiclassical nonlinear Schrodinger equations with potential and focusing initial data, preprint.

CarRa-p

R. Carles, J. Rauch, Focusing of spherical nonlinear pulses in R^{1+3} III. Sub and supercritical cases, preprint.

CrrBu1991

R. Carrol, C. Bu, Solution of the Forced Nonlinear Schrodinger Equation (NLS) Using PDE Techniques, Appl. Anal. 41 (1991), 31-51.

Cv2002

X. Carvajal, Propriedades das solucoes de uma equacao de Scrodinger nao linear de alta ordem, PhD Thesis, Instituto de matematica pura e aplicada, IMPA, Rio de Janeiro, Brazil, (2002).

Cv2004

X. Carvajal, Local well-posedness for a higher order nonlinear Schrodinger equation in Sobolev spaces of negative indices , Electron. J. Diff. Eqns., Vol. 2004(2004), No. 13, pp. 1-10. </span>

CvLi2003

X. Carvajal, F. Linares, A higher order nonlinear Schr\"odinger equation with variable coefficients, Differential and Integral Equations, 16, 9, (2003), 1111\u20141130.</span>

CvLi-p

X. Carvajal, F. Linares, Some properties for a higher order nonlinear Schr\"odinger equation, Preprint.</span>

CvPan-p

X. Carvajal, M. Panthee, Unique continuation property for a higher</span>

• oder nonlinear Schr\"odinger equation, Preprint.

Ca1985

T. Cazenave, Uniform estimates for solutions of non-linear Klein-Gordon equations, J. Func. Anal. 60 (1985), 36-55.

Ca1989

T. Cazenave, An introduction to nonlinear Schrodinger equations, Textos de Metodes Matematicos 22 (Rio de Janeiro), 1989.

Ca1994

T. Cazenave, Blow up and scattering in the nonlinear Schrodinger equation, Textos de Metodes Mathematicos 30 (Rio de Janeiro), 1994.

CaHz1990

T. Cazenave, A. Haraux, Introduction aux problemes d'evolution semi-lineaires, SMAI, Ellipses (1990)

CaLo1982

T. Cazenave, P. Lions, Orbital stability of standing waves for some nonlinear Schrodinger equations, Comm. Math. Phys. 68 (1979), 209-243.

CaWe1990

T. Cazenave, F.B. Weissler, The Cauchy problem for the critical nonlinear Schrodinger equation, Non. Anal. TMA, 14 (1990), 807-836.

CaWe1992

T. Cazenave, F.B. Weissler, Rapidly decaying solutions of the nonlinear Schrodinger equation, Comm. Math. Phys. 47 (1992), 75-100.

CaWe1998

T. Cazenave, F.B. Weissler, Asymptotically self-similar global solutions of the nonlinear Schrodinger and heat equations, Math. Z. 228 (1998), 83-120.

CaWe1998b

T. Cazenave, F.B. Weissler, More self-similar global solutions of the nonlinear Schrodinger equation, Nonlinear Diff. Eq. Appl. 5 (1998), 355-365.

CaSaTv1998

T. Cazenave, J. Shatah, A.S. Tahvildar-Zadeh, Harmonic maps of the hyperbolic space and development of singularities in wave maps and Yang-Mills fields, Ann. Inst. H. Poincaré Phys. Théor.68 (1998), 315-349.

CaVeVi-p

T. Cazenave, L. Vega, M.C. Vilela, A note on the nonlinear Schrodinger equation in weak L^p spaces, preprint.

Chd1973

J.M. Chadam, Global solutions of the Cauchy problem for the (classical) Maxwell-Dirac equations in one space dimension, J. Funct. Anal 13. (1973), 173 - 184.

CgSaUh2000

N. Chang, J. Shatah, K. Uhlenbeck, Schrodinger maps, CPAM 52 (2000), 590-602

Ch2000

J.Y. Chemin, Explosion geometrique pour certaines equations d\u2019ondes nonlineaires [d\u2019apres Serge Alinhac], Seminaire Bourbaki Exp. 850, Asterique 266 (2000), 7-20.

Ci1994

H. Chihara, Local existence for the semilinear Schrodinger equations in one space dimension, J. Math. Kyoto Univ. 34 (1994), 353-367.

Ci1995

H. Chihara, Local existence for semilinar Schrodinger equations, Math. Japon. 42 (1995), 35-52.

Ci1996

H. Chihara, The initial value problem for cubic semilinear Schrodinger equations, Publ. Res. Inst. Math. Sci. 32 (1996), 445-471.

Ci1999

H. Chihara, Gain of regularity for semilinear Schrodinger equations, Math. Ann. 315 (1999), 529-567.

Ci2002

H. Chihara, The initial value problem for Schrodinger equations on the torus, IMRN 15 (2002), 789-820.

Ci-p

H. Chihara, Third order semilinear dispersive equations related to deep water waves, preprint.

Chp1993

M.W. Choptuik, Phys. Rev. Lett. 70 (1993), 9

Cq1952

Y. Choquet-Bruhat, Theorem d\u2019Existence pour certains sytemes d\u2019equations aux derivees partielles nonlineaires, Acta Math 88 (1952), 141-225

Cq1973

Y. Choquet-Bruhat, Un theoreme d\u2019instabilit pour certains equations hyperboliques nonlineaires, C.R. Acad. Paris Sr. A-B 276 (1973), A281-A284.

Cq1987

Y. Choquet-Bruhat, Global existence theorems for hyperbolic harmonic maps, Ann. Inst. H. Poincare Phys. Theor. 46 (1987), 97-111.

Cq2000

Y. Choquet-Bruhat, The null condition and asymptotic expansions for Einstein\u2019s equations, Ann. Phys. (Leipzig) 9 (2000), 258-266.

Cq-p

Y. Choquet-Bruhat, Wave maps in general relativity, preprint.

Cq-p2

Global wave maps on curved space times, preprint.

CqCd1981

Y. Choquet-Bruhat, D. Christodoulou, Existence of global solutions of the Yang-Mills, Higgs, and spinor field equations in 3+1 dimensions, Ann. Sci. Ecole Norm. Sup. (4) 14 (1981), 481-506.

CqGc1969

Y. Choquet-Bruhat, R. Geroch, Global aspects of the Cauchy problem in General Relativity, CMP 14 (1969), 329-335.

CtCoTa-p

M. Christ, J. Colliander, T. Tao, Asymptotics, frequency modulation, and low-regularity illposedness of canonical defocussing equations, preprint.

CtCoTa-p2

M. Christ, J. Colliander, T. Tao, Low-regularity ill-posedness for nonlinear Schrodinger and wave equations, preprint.

CtCoTa-p3

M. Christ, J. Colliander, T. Tao, Instability of the periodic nonlinear Schrodinger equation, preprint.

CtWs1991

M. Christ, M. Weinstein, Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation, J. Funct. Anal. 100 (1991), 87-109.

Cd1981

D. Christodoulou, Solutions globales des equations de champ de Yang-Mills, C. R. Acad. Sci. Paris Series A 289 (1981), 481-506.

Cd1986

D. Christodoulou, Global solutions of nonlinear hyperbolic equations for small initial data, Comm. Pure Appl. Math, 39 (1986), 267-282.

CdKl1990

D. Christodoulou, S. Klainerman, Asymptotic properties of linear field equations in Minkowski space, Comm. Pure Appl. Math, (1990), 137-199

CdKl1993

D. Christodoulou, S. Klainerman, The global nonlinear stability of the Minkowski space, Princeton Mathematical Series 41 (1993)

CdTv1993

D. Christodoulou, A. Tahvildar-Zadeh, On the regularity of spherically symmetric wave maps, Comm. Pure Appl. Math, 46 (1993), 1041-1091.

CdTv1993b

D. Christodoulou, A. Tahvildar-Zadeh, On the asymptotic behavior of a spherically symmetric wave map, Duke Math. J. 71 (1993), 31-69.

CcSa1997

P. Chrusciel, J. Shatah, Global existence of solutions of the Yang-Mills equations on globally hyperbolic four-dimensional Lorentzian manifolds Asian J. Math. 1 (1997), no. 3, 530-548.

Coh1992

S. Cohn, Resonance and long time existence for the quadratic nonlinear Schrodinger equation, CPAM 45 (1992), 973-1001.

Coh1994

S. Cohn, Global existence for the nonresonant Schrodinger equation in two space dimensions, Canad. Appl. Math. Quart. 2 (1994), 257-282.

CoiWic1990

R. Coifman, V. Wickerhauser, The scattering transform for the Benjamin-Ono equation, Inverse Problems (1990) 6, 825-861.

Cn1993

T. Colin, Effects regularisants pour des equations dispersive obtenus par une transformee de Wigner generalisee, C. R. Acad. Sci. Paris, Ser. I. Math 317 (1993), 673-676.

Col2002

M. Colin, On the local well-posedness of quasilinear Schrodinger equations in arbitrary space dimension, CPDE 27 (2002), 325-354.

Col2003

M. Colin, Stability of stationary waves for a quasilinear Schrödinger equation in space dimension 2. Adv. Differential Equations 8 (2003), no. 1, 1--28.

Co1996

J. Colliander, Globalizing estimates for the KP-I equation, Illinois J. Math. 40 (1996), 692-698.

Co1997

J. Colliander, The initial value problem for the Zakharov system, PhD Thesis, U. Illinois, 1997.

CoDeKnSt-p

J. Colliander, J. Delort, C. Kenig, G. Staffilani, Bilinear Estimates and applications to 2D NLS, preprint.

CoKeStTkTa2001

J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, Global well-posedness for KdV in Sobolev spaces of negative index, EJDE 2001 (2001) No 26, 1-7.

CoKeStTkTa2001b

J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, Global well-posedness for the Schrodinger equations with derivative, SIAM J. Math. Anal. 33 (2001), 649-669.

CoKeStTkTa2002

J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, Almost conservation laws and global rough solutions to a nonlinear Schrodinger equation, Math Res. Lett. 9 (2002), 5-6, 659-682.

CoKeStTkTa2002b

J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, A refined global well-posedness for the Schrodinger equations with derivative, SIAM J. Math. Anal. 34 (2002), 64-86.

CoKeStTkTa2003

J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, [math.AP/0110045 Sharp global well-posedness results for periodic and non-periodic KdV and modified KdV on R and T], JAMS 16 (2003), 705-749.

CoKeStTkTa2003b

J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, Polynomial upper bounds for the orbital instability of the 1D cubic NLS below the energy norm, Discrete Contin. Dyn. Syst. 9 (2003), 31-54.

CoKeStTkTa2003c

J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, Polynomial growth and orbital instability bounds for $L^2$-subcritical NLS below the energy norm, Commun. Pure Appl. 2 (2003), 33-50.

CoKeStTkTa-p

J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, Global well-posedness and scattering in the energy space for the critical nonlinear Schrodinger equation in R^3, preprint

CoKeStTkTa-p3

J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, Multi-linear estimates for periodic KdV equations, and applications, preprint

CoKeStTkTa-p5

J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, Further global well-posedness results for 2D NLS, preprint.

CoKeStTkTa-p8

J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, Scattering for cubic 3D NLS below the energy norm, preprint.

CoKeStTkTa-p9

J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T. Tao, Symplectic non-squeezing for periodic KdV, preprint

CoKn-p

J. Colliander, C. Kenig, The generalized Korteweg-de Vries equation on the half line, preprint

CoKnSt-p

J. Colliander, C. Kenig, G. Staffilani, Local well-posedness and regularity properties of solutions of the generalized Kadomtsev-Petviashvili equations, preprint.

CoKnSt-p2

J. Colliander, C. Kenig, G. Staffilani, Low regularity solutions of the Kadomtsev-Petviashvili-I equation, preprint.

CoKnSt-p3

J. Colliander, C. Kenig, G. Staffilani, Small solutions for the Kadomtsev-Petviashvili I equation, Mosc. Math J. 1 (2001), 491-520.

CoKnSt-p4

J. Colliander, C. Kenig, G. Staffilani, Local well-posedness for dispersion generalized Benjamin-Ono equations, preprint.

=====CoStTk1999===== J. Colliander, G. Staffilani, H. Takaoka, Global well-posedness of the KdV equation below L^2], Math Res. Letters 6 (1999), 755-778

CoSt-p

J. Colliander, G. Staffilani, Regularity bounds on Zakharov System evolutions, EJDE 2002 (2002) No 75, 1-11.

ConSau1988

P. Constantin, J.C. Saut, Local smoothing properties of dispersive equations, J. Amer. Math. Soc. 1 (1988), 413-439.

ConSau1989

P. Constantin, J.C. Saut, Local smoothing properties of Schrodinger equations, Indiana U. Math. J. 38 (1989), 781-810.

CkGr-p

G. Costakis, M. Grillakis, Local and global existence for the Schrodinger map problem, preprint

CrKpSr1992

W. Craig, T. Kappeler, W. Strauss, Gain of regularity for equations of the Korteweg-de Vries type, Ann. Inst. Henri Poincare 9 (1992), 147-186.

CrKpSr1995

W. Craig, T. Kappeler, W. Strauss, Microlocal dispersive smoothing for the Schrodinger equation, Comm. Pure Appl. Math 48 (1995), 769-860.

Cs1980

C. Cronstrom, A simple and complete Lorentz-invariant gauge condition, Phys. Lett. B 90 (1980), 267-269.

Cu1999

S. Cuccagna, On the local existence for the Maxwell-Klein-Gordon system in R^{3+1}, Comm. Partial Differential Equations. 24 (1999), 851-867.

Cu2001

S. Cuccagna, Stabilization of solutions to nonlinear Schrodinger equations, CPAM 54 (2001), 1110-1145.

Cu2001p

S. Cuccagna, On asymptotic stability of ground states of NLS, preprint.

DanGe-p

P. D'Ancona, V. Georgiev, On the continuity of the solution operator of the wave maps system, preprint

DanPie-p

P. D\u2019Ancona, V. Pierfelice, On the wave equation with large rough potential, preprint.

DaKn1982

B. Dahlberg, C. E. Kenig, A note on the almost everywhere behaviour of solutions to the Schrodinger equation, Harmonic Analysis, Lecture Notes in Math., Springer Verlag, 908, (1982), 205-208.

Dt1990

P. Datti, Nonlinear wave equations in exterior domains, Nonlinear Anal. 15 (1990), 321-331.

DavSte1974

A. Davey, K. Stewartson, On three dimensional packets of surface waves, Proc. R. Soc. A 338 (1974), 101-110.

DbDM2002

A. Debussche, L. Di Menza, Numerical simulation of the nonlinear stochastic Schrodinger equation, Phys D 162 (2002), 131-154.

DfZx1994

P. Deift, X. Zhou, Long-time asymptotics for integrable systems. Higher order theory, Comm. Math. Phys. 165 (1994), 175-191.

De1997

J. Delort, Sur le temps d'existence pour l'equation de Klein-Gordon semi-lineaire en dimension 1, Bull. Soc. Math. France 125 (1997), 269-311.

De1997b

J. Delort, L'équation de Klein-Gordon à données petites faiblement décroissantes, Séminaire sur les Équations aux Dérivées Partielles, 1996-1997, Exp. No. V, 14 pp., École Polytech., Palaiseau, 1997.

De1998

J. Delort, Temps d'existence pour l'équation de Klein-Gordon semi-linéaire à données petites périodiques, Amer. J. Math. 120 (1998), 663-689.

De1999

J. Delort, Minoration du temps d'existence pour l'équation de Klein-Gordon non-linéaire en dimension 1 d'espace, Ann. Inst. H. Poincaré Anal. Non Linéaire 16 (1999), 563-591.

De2001

J. Delort, Existence global et comportement asymptotique pour l'equation de Klein-Gorodn quasi lineaire a donnees petites en dimension 1, Ann. Sci. Ecole Norm. Sup. 34 (2001), 1-61.

De2002

J. Delort, Global solutions for small nonlinear long-range perturbations of two-dimensional Schrodinger equations, Societe Mathematique de France.

DeFg-p

J. Delort, D. Fang, Almost global existence of solutions of semilinear Klein-Gordon equations with small weakly decaying Cauchy data, CPDE to appear.

DeFgXue-p

J. Delort, D. Fang, R. Xue, Global existence of small solutions for quadratic quasilinear Klein-Gordon systems in two space dimensions, preprint.

DeSze-p

J. Delort, J. Szeftel, Long time existence for small data nonlinear Klein-Gordon equations on tori and spheres, IMRN 2004:37 (2004) 1897-1966

DiaFi1989

J. Dias, M. Figueira, On the existence of weak solutions for a time-dependent nonlinear Dirac equation, Proc. Royal Soc. Edinburgh 113A (1989), 149-158.

Di1998

Q. Ding, A note on the NLS and the Schrodinger flow of maps, Phys. Lett A. 248 (1998) 49-56.

Di1999

Q. Ding, The gauge equivalence of the NLS and the Schrodinger flow of maps in 2+1 dimensions, J. Phys. Math. A.; Math. Gen. 32 (1999), 5087-5096.

Di-p

Q. Ding, On Schrodinger flows to the Hyperbolic 2-space, preprint.

Di2002

W. Ding, On the Schrodinger flows, Proc. ICM Beijing 2002, vol 2, 283-292.

DiWgy1998

W. Ding, Y. Wang, Schrodinger flow of maps into symplectic manifolds, Science in China (Series A) 41 (1998), 746-755.

DiWgy2001

W. Ding, Y. Wang, Local Schrodinger flow into Kahler manifolds. Science in China (Series A) 44 (2001), 1446-1464.

Do1994

S. Doi, On the Cauchy problem for Schrodinger type equations and the regularity of the solutions, J. Math. Kyoto U. 34 (1994), 319-328.

Do1996

S. Doi, Remarks on the Cauchy problem for Schrodinger type equations, CPDE 21 (1996), 163-178.

Do2000

S. Doi, Smoothing effects for Schrodinger evolution equation and global behavior of geodesic flow, Math Ann. 318 (2000), 355-389.

Do-p

S. Doi, On the regularity of solutions for some semilinear Schrodinger equations, preprint.

DonLs1981

G.C. Dong, S.J. Li, On the initial value problem for a nonlinear Schrodinger equation, JDE 42 (1981) 353-365.

Du1982

O. Dumitrascu, Equivariant solutions of the Yang-Mills equations. (Romanian. English summary) Stud. Cerc. Mat. 34 (1982), 329-333.

Duy-p

T. Duyckaerts, A singular critical potential for the Schrodinger operator, preprint.

Dy1979

K.B. Dysthe, Note on a modification to the nonlinear Schrodinger equation for application to deep water, Proc. Roy. Soc. London Ser. A. 369 (1979), 105\u2014114.

EaMc1982

D. Eardley, V. Moncrief, The global existence of Yang-Mills-Higgs fields in R^{3+1}, Comm. Math. Phys. 83 (1982), 171-212.

EckShr1983

W. Eckhaus, P. Schuur, The emergence of solutions to the Korteweg-de Vries equation from arbitrary initial conditions, Math Meth. Appl. Sci. 5 (1983), 97-116.

El2003

K. El Dika, Stabilite asymptotique des ondes solitaires de l\u2019equation de Benjamin-Bona-Mahony, C. R. Acad. Sci. Paris Ser. I 337 (2003), 649\u2014652.

El-p

K. El Dika, Asymptotic stability of solitary waves for the Benjamin-Bona-Mahony equation, Preprint 2003.

EscVe1997

M. Escobedo, L. Vega, A semilinear Dirac equation in H^s(R^3) for s > 1, Siam J. Math Anal. 28 (1997), 338-362.

EsSer2002

M. Esteban, E. Sere, An overview of linear and nonlinear Dirac equations, Discrete Cont. Dynamical Systems 8 (2002), 381-397.

EsSr1994

M. Esteban, W. Strauss, Nonlinear bound states outside an insulated sphere, CPDE 19 (1994), 177-194.

FgGl1996

Y. Fang, M. Grillakis, A priori estimates for the 2-D wave equation. Comm. Partial Differential Equations 21 (1996), no. 9-10, 1643-1665.

Fa1983

A. Faminskii, The Cauchy problem and the mixed problem in the half strip for equations of Korteweg-de Vries type (Russian), Dinamika Sploshn. Sre