Startseite Inverse scattering transform in two spatial dimensions for the N-wave interaction problem with a dispersive term
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Inverse scattering transform in two spatial dimensions for the N-wave interaction problem with a dispersive term

  • Mansur I. Ismailov EMAIL logo
Veröffentlicht/Copyright: 28. Juli 2021

Abstract

A dispersive N-wave interaction problem ( N = 2 n ), involving n velocities in two spatial and one temporal dimensions, is introduced. Explicit solutions of the problem are provided by using the inverse scattering method. The model we propose is a generalization of both the N-wave interaction problem and the ( 2 + 1 ) matrix Davey–Stewartson equation. The latter examines the Benney-type model of interactions between short and long waves. Referring to the two-dimensional Manakov system, an associated Gelfand–Levitan–Marchenko-type, or so-called inversion-like, equation is constructed. It is shown that the presence of the degenerate kernel reads explicit soliton-like solutions of the dispersive N-wave interaction problem. We also present a discussion on the uniqueness of the solution of the Cauchy problem on an arbitrary time interval for small initial data.

Acknowledgements

We gratefully acknowledge the anonymous referees for their valuable comments which definitely make this paper more correct and easy to read.

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Received: 2020-08-21
Revised: 2021-03-01
Accepted: 2021-05-20
Published Online: 2021-07-28
Published in Print: 2021-10-01

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