Pseudoconformal Transformation

The pseudoconformal transformation

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle u(t,x) \to v(\tau, y) = \frac{|\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 $L_{x}^{2}$ and on $L^{2}$-admissible Strichartz spaces $L_{\tau }^{q}L_{y}^{r}$.