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The inverse problem for some special spectral data

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  • Vakhnenko, V.O.
  • Parkes, E.J.

Abstract

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 suggested 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.

Suggested Citation

  • Vakhnenko, V.O. & Parkes, E.J., 2016. "The inverse problem for some special spectral data," Chaos, Solitons & Fractals, Elsevier, vol. 82(C), pages 116-124.
    • Handle: RePEc:eee:chsofr:v:82:y:2016:i:c:p:116-124
    DOI: 10.1016/j.chaos.2015.11.012
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    1. Vakhnenko, V.O. & Parkes, E.J., 2012. "The singular solutions of a nonlinear evolution equation taking continuous part of the spectral data into account in inverse scattering method," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 846-852.
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