Existence of Chaos for a Singularly Perturbed NLS Equation
| dc.creator | Li, Yanguang Charles | |
| dc.date | 2002-06-25 | |
| dc.date.accessioned | 2026-07-07T04:49:22Z | |
| dc.date.available | 2026-07-07T04:49:22Z | |
| dc.description | The work [Li,99] is generalized to the singularly perturbed nonlinear Schrödinger (NLS) equation of which the regularly perturbed NLS studied in [Li,99] is a mollification. Specifically, the existence of Smale horseshoes and Bernoulli shift dynamics is established in a neighborhood of a symmetric pair of Silnikov homoclinic orbits under certain generic conditions, and the existence of the symmetric pair of Silnikov homoclinic orbits has been proved in [Li,01]. The main difficulty in the current horseshoe construction is introduced by the singular perturbation $\e \pa_x^2$ which turns the unperturbed reversible system into an irreversible system. It turns out that the equivariant smooth linearization can still be achieved, and the Conley-Moser conditions can still be realized. | |
| dc.identifier | https://arxiv.org/abs/math/0206270 | |
| dc.identifier | http://arxiv.org/abs/math/0206270 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64395 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Dynamical Systems | |
| dc.subject | 35Q55, 35Q30 | |
| dc.title | Existence of Chaos for a Singularly Perturbed NLS Equation | |
| dc.type | text |