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

V.O. Vakhnenko, E.J. Parkes

Research output: Contribution to journalArticle

5 Citations (Scopus)

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.
LanguageEnglish
Pages593-613
Number of pages21
JournalProgress of Theoretical Physics
Volume127
Issue number4
DOIs
Publication statusPublished - Apr 2012

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continuous spectra
inverse scattering
solitary waves
interactions

Keywords

  • inverse scattering
  • Vakhnenko-Parkes equation
  • discrete spectrum
  • continuous spectrum

Cite this

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Solutions associated with discrete and continuous spectrums in the inverse scattering method for the Vakhnenko-Parkes equation. / Vakhnenko, V.O.; Parkes, E.J.

In: Progress of Theoretical Physics, Vol. 127, No. 4, 04.2012, p. 593-613.

Research output: Contribution to journalArticle

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