The inverse problem for some special spectral data

V.O. Vakhnenko, E.J. Parkes

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In this paper the spectral problem of third order for the inverse scattering transform (IST) method is solved. For the discrete part of the spectral data, the two-multiple poles are taken into account. The line spectrum of continuum states for the IST method is examined as well. The suggested spectrum approximates in first order the step-function. The scope for the sug- gested
spectral data is demonstrated through the analysis of the Vakhnenko–Parkes equation that allows new solutions to be obtained. The account of the time-dependence is different from the standard procedure.
Original languageEnglish
Pages (from-to)116-124
Number of pages9
JournalChaos, Solitons and Fractals
Early online date30 Nov 2015
Publication statusPublished - 1 Jan 2016


  • inverse problem
  • spectral data
  • two-multiple poles
  • line spectrum of continuum states


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