Title

On The Long-Time Limit Of Semiclassical (Zero Dispersion Limit) Solutions Of The Focusing Nonlinear Schrödinger Equation: Pure Radiation Case

Abstract

In a previous paper [13] we calculated the leading-order term q 0(x, t, ε) of the solution of q(x, t, ε), the focusing nonlinear (cubic) Schrödinger (NLS) equation in the semiclassical limit (ε → 0) for a certain one-parameter family of initial conditions. This family contains both solitons and pure radiation. In the pure radiation case, our result is valid for all times t ≥ 0. The aim of the present paper is to calculate the long-term behavior of the semiclassical solution q(x, t, ε) in the pure radiation case. As before, our main tool is the Riemann-Hilbert problem (RHP) formulation of the inverse scattering problem and the corresponding system of "moment and integral conditions," known also as a system of "modulation equations." © 2006 Wiley Periodicals, Inc.

Publication Date

1-1-2006

Publication Title

Communications on Pure and Applied Mathematics

Volume

59

Issue

10

Number of Pages

1379-1432

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1002/cpa.20142

Socpus ID

33748300603 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/33748300603

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