Nonlinear Schrodinger equations with repulsive harmonic potential and applications
| dc.creator | Carles, Remi | |
| dc.date | 2002-10-31 | |
| dc.date | 2003-03-14 | |
| dc.date.accessioned | 2026-07-07T04:52:32Z | |
| dc.date.available | 2026-07-07T04:52:32Z | |
| dc.description | We study the Cauchy problem for Schrodinger equations with repulsive quadratic potential and power-like nonlinearity. The local problem is well-posed in the same space as that used when a confining harmonic potential is involved. For a defocusing nonlinearity, it is globally well-posed, and a scattering theory is available, with no long range effect for any superlinear nonlinearity. When the nonlinearity is focusing, we prove that choosing the harmonic potential sufficiently strong prevents blow-up in finite time. Thanks to quadratic potentials, we provide a method to anticipate, delay, or prevent wave collapse; this mechanism is explicit for critical nonlinearity. | |
| dc.description | Final version, to appear in SIAM J. Math. Anal | |
| dc.identifier | https://arxiv.org/abs/math/0210481 | |
| dc.identifier | http://arxiv.org/abs/math/0210481 | |
| dc.identifier | SIAM J. Math. Anal., 35, #4 (2003), 823-843. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65496 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Mathematical Physics | |
| dc.subject | 35Q55; 35B05; 35B40; 35P25 | |
| dc.title | Nonlinear Schrodinger equations with repulsive harmonic potential and applications | |
| dc.type | text |