Modulation theory for self-focusing in the nonlinear Schrödinger-Helmholtz equation
| dc.creator | Cao, Yanping | |
| dc.creator | Musslimani, Ziad H. | |
| dc.creator | Titi, Edriss S. | |
| dc.date | 2008-11-23 | |
| dc.date | 2009-02-08 | |
| dc.date.accessioned | 2026-07-07T12:38:30Z | |
| dc.date.available | 2026-07-07T12:38:30Z | |
| dc.description | The nonlinear Schrödinger-Helmholtz (SH) equation in $N$ space dimensions with $2σ$ nonlinear power was proposed as a regularization of the classical nonlinear Schrödinger (NLS) equation. It was shown that the SH equation has a larger regime ($1\leσ<\frac{4}{N}$) of global existence and uniqueness of solutions compared to that of the classical NLS ($0<σ<\frac{2}{N}$). In the limiting case where the Schrödinger-Helmholtz equation is viewed as a perturbed system of the classical NLS equation, we apply modulation theory to the classical critical case ($σ=1,\:N=2$) and show that the regularization prevents the formation of singularities of the NLS equation. Our theoretical results are supported by numerical simulations | |
| dc.description | new article, 20 pages, 10 figures, to appear in Numerical Functional Analysis and Optimization | |
| dc.identifier | https://arxiv.org/abs/0811.3729 | |
| dc.identifier | http://arxiv.org/abs/0811.3729 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/218783 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 35Q40, 35Q55, 78A60 | |
| dc.title | Modulation theory for self-focusing in the nonlinear Schrödinger-Helmholtz equation | |
| dc.type | text |