Inverse scattering transform for N-wave interaction problem with a dispersive term in two spatial dimensions
Abstract
In this work, we introduce a dispersive N(=2n)-wave interaction problem involving n velocities in two spatial dimensions and one temporal dimension. Exact solutions of the problem are exhibited. This is a generalization of the N-wave interaction problem and matrix Davey-Stewartson equation with 2+1 dimensions that examines the Benney-type model of interactions between short and long waves. Accordingly, associated with the solutions of two dimensional analog of the Manakov system, a Gelfand-Levitan-Marchenko (GLM)-type, or so-called inversion-like, equation is constructed. It is shown that the presence of the degenerate kernel reads exact soliton-like solutions of the dispersive N-wave interaction problem.We also mention the unique solution of the Cauchy problem on an arbitrary time interval for small initial data.
Cite
@article{arxiv.2008.09334,
title = {Inverse scattering transform for N-wave interaction problem with a dispersive term in two spatial dimensions},
author = {Mansur I Ismailov},
journal= {arXiv preprint arXiv:2008.09334},
year = {2020}
}