On semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrodinger equation

    Authors

    A. Tovbis; S. Venakides;X. Zhou

    Comments

    Authors: contact us about adding a copy of your work at STARS@ucf.edu

    Abbreviated Journal Title

    Commun. Pure Appl. Math.

    Keywords

    KORTEWEG-DEVRIES EQUATION; VARYING EXPONENTIAL WEIGHTS; SHABAT; EIGENVALUE PROBLEM; ASYMPTOTICS; POLYNOMIALS; RESPECT; GENERATION; POTENTIALS; Mathematics, Applied; Mathematics

    Abstract

    We calculate the leading-order term of the solution of the focusing nonlinear (cubic) Schrodinger 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 greater than or equal to 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. (C) 2004 Wiley Periodicals, Inc.

    Journal Title

    Communications on Pure and Applied Mathematics

    Volume

    57

    Issue/Number

    7

    Publication Date

    1-1-2004

    Document Type

    Article

    Language

    English

    First Page

    877

    Last Page

    985

    WOS Identifier

    WOS:000221575500002

    ISSN

    0010-3640

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