Pseudoconformal Transformation

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The pseudoconformal transformation

u(t,x) \to v(\tau, y) = |\tau|^{-\frac{d}{2}} e^{\frac{i |y|^2}{4t}} u ( - \frac{1}{\tau} , \frac{y}{\tau})

maps solutions of the mass critical NLS to solutions. The pseudoconformal image of a soliton is an explicit blowup solution. The pseudoconformal transformation is an isometry on L^2_x and on L2-admissible Strichartz spaces L^q_\tau L^r_y.

Retrieved from "http://tosio.math.toronto.edu/wiki/index.php/Pseudoconformal_Transformation"
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