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

    Authors

    A. Tovbis; S. Venakides;X. Zhou

    Comments

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    Abbreviated Journal Title

    Commun. Pure Appl. Math.

    Keywords

    ASYMPTOTICS; Mathematics, Applied; Mathematics

    Abstract

    In a previous paper [13] we calculated the leading-order term q(0)(x, t, epsilon) of the solution of q (x, t, epsilon), the focusing nonlinear (cubic) Schrodinger (NLS) equation in the semiclassical limit (epsilon - > 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, epsilon) 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." (c) 2006 Wiley Periodicals, Inc.

    Journal Title

    Communications on Pure and Applied Mathematics

    Volume

    59

    Issue/Number

    10

    Publication Date

    1-1-2006

    Document Type

    Article

    Language

    English

    First Page

    1379

    Last Page

    1432

    WOS Identifier

    WOS:000239775600001

    ISSN

    0010-3640

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