Title

On Semiclassical (Zero Dispersion Limit) Solutions Of The Focusing Nonlinear Schrödinger Equation

Abstract

We calculate the leading-order term of the solution of the focusing nonlinear (cubic) Schrödinger equation (NLS) in the semiclassical limit 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. We utilize the Riemann-Hilbert problem formulation of the inverse scattering problem to obtain the leading-order term of the solution. Error estimates are provided. © 2004 Wiley Periodicals, Inc.

Publication Date

7-1-2004

Publication Title

Communications on Pure and Applied Mathematics

Volume

57

Issue

7

Number of Pages

877-985

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1002/cpa.20024

Socpus ID

2942535891 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/2942535891

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