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On semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrödinger equation
Author(s) -
Tovbis Alexander,
Venakides Stephanos,
Zhou Xin
Publication year - 2004
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20024
Subject(s) - semiclassical physics , limit (mathematics) , mathematics , nonlinear schrödinger equation , zero (linguistics) , nonlinear system , dispersion (optics) , mathematical physics , initial value problem , mathematical analysis , inverse scattering problem , inverse problem , schrödinger equation , physics , quantum mechanics , quantum , linguistics , philosophy
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.