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arXiv · 1006.4909

Long-Time Asymptotics for Solutions of the NLS Equation with a Delta Potential and Even Initial Data

Percy Deift·Jungwoon Park
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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-Hilbert problems introduced by Deift and Zhou. Our work strengthens, and extends, earlier work on the problem by Holmer and Zworski.

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Percy Deift, Jungwoon Park. 2010-06-28. Long-Time Asymptotics for Solutions of the NLS Equation with a Delta Potential and Even Initial Data. https://doi.org/10.1007/s11005-010-0458-5

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