Long-Time Asymptotics for Solutions of the NLS Equation with a Delta Potential and Even Initial Data: Announcement of Results |
| |
Authors: | Percy Deift Jungwoon Park |
| |
Affiliation: | 1. Courant Institute of Mathematical Sciences, New York University, New York, NY, USA
|
| |
Abstract: | We consider the one-dimensional focusing nonlinear Schrödinger equation (NLS) with a delta potential and even initial data. The problem is equivalent to the solution of the initial/boundary problem for NLS on a half-line with Robin boundary conditions at the origin. We follow the method of Bikbaev and Tarasov which utilizes a Bäcklund transformation to extend the solution on the half-line to a solution of the NLS equation on the whole line. We study the asymptotic stability of the stationary 1-soliton solution of the equation under perturbation by applying the nonlinear steepest-descent method for Riemann?CHilbert problems introduced by Deift and Zhou. Our work strengthens, and extends, the earlier work on the problem by Holmer and Zworski. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|