On the role of quadratic oscillations in nonlinear Schroedinger equations II. The $L^2$-critical case
| dc.creator | Carles, Remi | |
| dc.creator | Keraani, Sahbi | |
| dc.date | 2004-04-09 | |
| dc.date | 2004-09-06 | |
| dc.date.accessioned | 2026-07-07T06:33:04Z | |
| dc.date.available | 2026-07-07T06:33:04Z | |
| dc.description | We consider a nonlinear semi-classical Schroedinger 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 concern the $L^2$-critical case, in space dimensions 1 and 2; we describe the set of non-linearizable data, which is larger, due to the scaling. As an application, we precise a result by F. Merle and L. Vega concerning finite time blow up for the critical Schroedinger equation. The proof relies on linear and nonlinear profile decompositions. | |
| dc.description | More explanations | |
| dc.identifier | https://arxiv.org/abs/math/0404201 | |
| dc.identifier | http://arxiv.org/abs/math/0404201 | |
| dc.identifier | Trans. Amer. Math. Soc. 359 (2007), 33-62. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99073 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Primary 35Q55; Secondary 35B40, 35B05 | |
| dc.title | On the role of quadratic oscillations in nonlinear Schroedinger equations II. The $L^2$-critical case | |
| dc.type | text |