A single pole and a duble pole in the inverse scattering transform method

1Vakhnenko, VO
1S. I. Subbotin Institute of Geophysics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2017, 7:10-17
Section: Mathematics
Language: Ukrainian

For the discrete part of spectral data in the inverse scattering transform method, the double poles and a single pole are taken into account. The scope of application for the suggested spectral data is demonstrated through the analysis of the Vakhnenko—Parkes equation that allows new solutions to be obtained. This approach can be applied to other integrable nonlinear equations.

Keywords: double poles, inverse problem, spectral data
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