On the role of quadratic oscillations in nonlinear Schrödinger equations II. The $L^2$-critical case
On the role of quadratic oscillations in nonlinear Schrödinger equations II. The $L^2$-critical case
We consider a nonlinear semi-classical Schrödinger equation for which quadratic oscillations lead to focusing at one point, described by a nonlinear scattering operator. The relevance of the nonlinearity was discussed by R. Carles, C. Fermanian–Kammerer and I. Gallagher for $L^2$-supercritical power-like nonlinearities and more general initial data. The present results …