Focusing Schrödinger lens ansatz

If $P_{\eta }$ solves the trapped focusing cubic ground-state equation, the ansatzsolves the two-dimensional mass-critical focusing nonlinear Schrödinger equation when

The initial conditions $\lambda (-1)=\sqrt{1+\eta }$ and $b(-1)=1$ selectThe scale grows linearly at infinity, yielding a finite critical spacetime norm for the corresponding lens solution.