On the long-time limit of semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrödinger equation: Pure radiation case

Journal Article (Journal Article)

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.

Full Text

Duke Authors

Cited Authors

  • Tovbis, A; Venakides, S; Zhou, X

Published Date

  • January 1, 2006

Published In

Volume / Issue

  • 59 / 10

Start / End Page

  • 1379 - 1432

Electronic International Standard Serial Number (EISSN)

  • 0010-3640

International Standard Serial Number (ISSN)

  • 0010-3640

Digital Object Identifier (DOI)

  • 10.1002/cpa.20142

Citation Source

  • Scopus