The inverse problem for some special spectral data

Vakhnenko, V.O. and Parkes, E.J. (2016) The inverse problem for some special spectral data. Chaos, Solitons and Fractals, 82. pp. 116-124. ISSN 0960-0779

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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.