Semiclassical Soliton Ensembles for the Focusing Nonlinear Schroedinger Equation
| dc.creator | Kamvissis, S. | |
| dc.creator | McLaughlin, K. T. -R. | |
| dc.creator | Miller, P. D. | |
| dc.date | 2000-12-16 | |
| dc.date.accessioned | 2026-07-07T05:33:13Z | |
| dc.date.available | 2026-07-07T05:33:13Z | |
| dc.description | We present a new generalization of the steepest descent method introduced by Deift and Zhou for matrix Riemann-Hilbert problems and use it to study the semiclassical limit of the focusing nonlinear Schroedinger equation with real analytic, even, bell-shaped initial data. We provide explicit strong locally uniform asymptotics for a sequence of exact solutions corresponding to initial data that has been modified in an asymptotically small sense. We call this sequence of exact solutions a semiclassical soliton ensemble. Our asymptotics are valid in regions of the (x,t) plane where a certain scalar complex phase function can be found. We characterize this complex phase function directly by a finite-gap ansatz and also via the critical point theory of a certain functional; the latter provides the correct generalization of the variational principle exploited by Lax and Levermore in their study of the zero-dispersion limit of the Korteweg-de Vries equation. | |
| dc.description | 215 Pages. Submitted to Annals of Mathematics Studies | |
| dc.identifier | https://arxiv.org/abs/nlin/0012034 | |
| dc.identifier | http://arxiv.org/abs/nlin/0012034 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79920 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.title | Semiclassical Soliton Ensembles for the Focusing Nonlinear Schroedinger Equation | |
| dc.type | text |