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{{stub}} Informally, an equation is '''defocusing''' (or '''repulsive''') if the [[nonlinearity]] tends to act to dissipate the solution when it is concentrated, thus (in principle) reinforcing the effects of [[dispersion]]. The opposite of defocusing is [[focusing]], though there do exist nonlinear equations which are neither focusing nor defocusing as the nonlinearity exhibits no bias towards helping or hindering the dispersion. Defocusing equations tend to have an definite Hamiltonian and are less likely to blow up than focusing ones. They rarely support [[soliton]] solutions; instead, solitons tend to [[scatter]] to linear solutions. Defocusing equations also often enjoy [[monotonicity formula]]e which are unavailable in the focusing case. [[Category:Concept]]

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