Special singularity function for continuous part of the spectral data in the associated eigenvalue problem for nonlinear equations

V.O. Vakhnenko, E.J. Parkes

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

The procedure for finding the solutions of the Vakhnenko-Parkes equation by means
of the inverse scattering method is described. The continuous spectrum is taken into
account in the associated eigenvalue problem. The suggested special form of the
singularity function for continuous part of the spectral data gives rise to the multimode solutions. The sufficient conditions are proved in order that these solutions become real functions. The interaction of the N periodic waves is studied. The procedure is illustrated by considering a number of examples
LanguageEnglish
Number of pages11
JournalJournal of Mathematical Physics
Volume53
Issue number6
Early online date11 Jun 2012
DOIs
Publication statusPublished - 2012

Fingerprint

nonlinear equations
Eigenvalue Problem
Nonlinear Equations
eigenvalues
Singularity
Periodic Wave
Continuous Spectrum
Inverse Scattering
continuous spectra
inverse scattering
Sufficient Conditions
Interaction
interactions
Form

Keywords

  • eigenvalue problem
  • nonlinear equations
  • Vakhnenko-Parkes equation

Cite this

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Special singularity function for continuous part of the spectral data in the associated eigenvalue problem for nonlinear equations. / Vakhnenko, V.O.; Parkes, E.J.

In: Journal of Mathematical Physics, Vol. 53, No. 6, 2012.

Research output: Contribution to journalArticle

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