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

Research output: Contribution to journalArticle

11 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 languageEnglish
Pages (from-to)846-852
Number of pages7
JournalChaos, Solitons and Fractals
Volume45
Issue number6
Early online date4 Apr 2012
DOIs
Publication statusPublished - Jun 2012

Fingerprint

nonlinear evolution equations
Periodic Wave
Singular Solutions
Inverse Scattering
inverse scattering
Nonlinear Evolution Equations
Solitons
Bound States
Eigenvalue Problem
Periodic Solution
eigenvalues
solitary waves
Scattering
Singularity
scattering
Interaction
interactions
Form

Keywords

  • Vakhnenko–Parkes equation
  • inverse scattering
  • continuous spectrum

Cite this

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The singular solutions of a nonlinear evolution equation taking continuous part of the spectral data into account in inverse scattering method. / Vakhnenko, V.O.; Parkes, E.J.

In: Chaos, Solitons and Fractals, Vol. 45, No. 6, 06.2012, p. 846-852.

Research output: Contribution to journalArticle

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AU - Parkes, E.J.

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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.

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