The inverse problem for some special spectral data

V.O. Vakhnenko and E.J. Parkes

Chaos, Solitons & Fractals, 2016, vol. 82, issue C, 116-124

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.

Keywords: Inverse problem; Spectral data; Two-multiple poles; Line spectrum of continuum states (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:82:y:2016:i:c:p:116-124

DOI: 10.1016/j.chaos.2015.11.012

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