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

Vakhnenko, V.O. and Parkes, E.J. (2012) Solutions associated with discrete and continuous spectrums in the inverse scattering method for the Vakhnenko-Parkes equation. Progress of Theoretical Physics, 127 (4). pp. 593-613. (https://doi.org/10.1143/PTP.127.593)

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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.

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• Item metadata

  Item type:	Article
  ID code:	39586
  Dates:	Date Event April 2012 Published
  Subjects:	Science > Mathematics > Probabilities. Mathematical statistics
  Department:	Faculty of Science > Mathematics and Statistics
  Depositing user:	Pure Administrator
  Date deposited:	08 May 2012 08:59
  Last modified:	11 Apr 2024 00:41
  Related URLs:	http://ptp.ipap.jp/link?PTP/127/593/
  URI:	https://strathprints.strath.ac.uk/id/eprint/39586