The singular solutions of a nonlinear evolution equation taking continuous part of the spectral data into account in inverse scattering method

V.O. Vakhnenko; E.J. Parkes

doi:10.1016/j.chaos.2012.02.019

The singular solutions of a nonlinear evolution equation taking continuous part of the spectral data into account in inverse scattering method

V.O. Vakhnenko, E.J. Parkes

Mathematics And Statistics

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19 Citations (Scopus)

Abstract

A procedure for finding the solutions of the Vakhnenko–Parkes equation by means of the
inverse scattering method is described. Both the bound state spectrum and the continuous
spectrum are considered in the associated eigenvalue problem. The suggested special form of the singularity function gives rise to periodic solutions. The interaction of a soliton with a one-mode periodic wave is studied.

Original language	English
Pages (from-to)	846-852
Number of pages	7
Journal	Chaos, Solitons and Fractals
Volume	45
Issue number	6
Early online date	4 Apr 2012
DOIs	https://doi.org/10.1016/j.chaos.2012.02.019
Publication status	Published - Jun 2012

Keywords

Vakhnenko–Parkes equation
inverse scattering
continuous spectrum

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10.1016/j.chaos.2012.02.019

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abstract = "A procedure for finding the solutions of the Vakhnenko–Parkes equation by means of the inverse scattering method is described. Both the bound state spectrum and the continuous spectrum are considered in the associated eigenvalue problem. The suggested special form of the singularity function gives rise to periodic solutions. The interaction of a soliton with a one-mode periodic wave is studied.",

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AU - Parkes, E.J.

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N2 - A procedure for finding the solutions of the Vakhnenko–Parkes equation by means of the inverse scattering method is described. Both the bound state spectrum and the continuous spectrum are considered in the associated eigenvalue problem. The suggested special form of the singularity function gives rise to periodic solutions. The interaction of a soliton with a one-mode periodic wave is studied.

AB - A procedure for finding the solutions of the Vakhnenko–Parkes equation by means of the inverse scattering method is described. Both the bound state spectrum and the continuous spectrum are considered in the associated eigenvalue problem. The suggested special form of the singularity function gives rise to periodic solutions. The interaction of a soliton with a one-mode periodic wave is studied.

KW - Vakhnenko–Parkes equation

KW - inverse scattering

KW - continuous spectrum

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UR - http://www.igph.kiev.ua/vakhnenko/vakhnenko.html

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DO - 10.1016/j.chaos.2012.02.019

M3 - Article

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EP - 852

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

IS - 6

ER -

The singular solutions of a nonlinear evolution equation taking continuous part of the spectral data into account in inverse scattering method

Abstract

Keywords

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