View source for Pseudoconformal Transformation

The pseudoconformal transformation

<math> u(t,x) \longmapsto v(\tau, y) = \frac{|\tau|^{-\frac{d}{2}} e^{i |y|^2}{4t} u ( - \frac{1}{\tau} , \frac{y}{\tau}) </math>

maps solutions of the [[Mass critical NLS|mass critical NLS]] to solutions. The pseudoconformal image of a [[Soliton|soliton]] is an explicit [[Blowup solution|blowup solution]]. The pseudoconformal transformation is an isometry on <math>L^2_x</math> and on <math>L^2</math>-admissible [[Strichartz estimates|Strichartz spaces]] <math>L^q_\tau L^r_y</math>.