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Solutions associated with discrete and continuous spectrums in the inverse scattering method for the Vakhnenko-Parkes equation

Vakhnenko, V.O. and Parkes, E.J. (2012) Solutions associated with discrete and continuous spectrums in the inverse scattering method for the Vakhnenko-Parkes equation. Progress of Theoretical Physics, 127 (4). pp. 593-613.

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    Abstract

    In this paper the inverse scattering method is applied to the Vakhnenko-Parkes equation. We describe a procedure for using the inverse scattering transform to find the solutions that are associated with both the bound state spectrum and continuous spectrum of the spectral problem. The suggested special form of the singularity function gives rise to the multi-mode periodic solutions. Sufficient conditions are obtained in order that the solutions become real functions. The interaction of the solitons and multi-mode periodic waves is studied. The procedure is illustrated by considering a number of examples.

    Item type: Article
    ID code: 39586
    Keywords: inverse scattering, Vakhnenko-Parkes equation, discrete spectrum, continuous spectrum, Probabilities. Mathematical statistics
    Subjects: Science > Mathematics > Probabilities. Mathematical statistics
    Department: Faculty of Science > Mathematics and Statistics
    Related URLs:
    Depositing user: Pure Administrator
    Date Deposited: 08 May 2012 09:59
    Last modified: 04 Oct 2012 21:20
    URI: http://strathprints.strath.ac.uk/id/eprint/39586

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