Solutions Associated with Discrete and Continuous Spectrums in the Inverse Scattering Method for the Vakhnenko-Parkes Equation | Zendy

В.О. Вахненко | Zendy; E.J. Parkes | Zendy

Open Access

Solutions Associated with Discrete and Continuous Spectrums in the Inverse Scattering Method for the Vakhnenko-Parkes Equation

Author(s) -

В.О. Вахненко,

E.J. Parkes

Publication year - 2012

Publication title -

progress of theoretical physics

Language(s) - English

Resource type - Journals

eISSN - 1347-4081

pISSN - 0033-068X

DOI - 10.1143/ptp.127.593

Subject(s) - physics , inverse scattering transform , inverse , inverse scattering problem , spectrum (functional analysis) , continuous spectrum , scattering , singularity , mathematical analysis , bound state , function (biology) , mode (computer interface) , inverse problem , scattering theory , quantum mechanics , mathematics , geometry , evolutionary biology , biology , computer science , operating system

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

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