The eigenvalue problem for the focusing nonlinear Schrodinger equation: new solvable cases

    Authors

    A. Tovbis;S. Venakides

    Comments

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    Abbreviated Journal Title

    Physica D

    Keywords

    Zakharov-Shabat eigenvalue problem; semi-classical limit; focusing; nonlinear Schrodinger equation; hypergeometric functions; Mathematics, Applied; Physics, Multidisciplinary; Physics, Mathematical

    Abstract

    In this paper, we study the semi-classical limit of the Zakharov-Shabat eigenvalue problem for the focusing of NLS with some specific initial data. In all these cases, the eigenvalue problem is reduced to connection problems for the hypergeometric equation and for other classical equations. The special initial data [Suppl. Frog. Theor. Phys, 55 (1974) 284] is contained in our family of initial data, parameterized by a real parameter mu, as a particular case mu = 0. We find that beyond a certain value of the parameter mu, the pure-point spectrum becomes empty and all the scattering information is contained in the reflection coefficient. (C) 2000 Published by Elsevier Science B.V.

    Journal Title

    Physica D

    Volume

    146

    Issue/Number

    1-4

    Publication Date

    1-1-2000

    Document Type

    Article

    Language

    English

    First Page

    150

    Last Page

    164

    WOS Identifier

    WOS:000165117000005

    ISSN

    0167-2789

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