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Linear stability of elastic 2-line solitons for the KP-II equation

Analysis of PDEs 2023-07-20 v1 Mathematical Physics math.MP

Abstract

The KP-II equation was derived by Kadomtsev and Petviashvili to explain stability of line solitary waves of shallow water. Using the Darboux transformations, we study linear stability of 2-line solitons whose line solitons interact elastically each other. Time evolution of resonant continuous eigenfunctions is described by a damped wave equation in the transverse variable which is supposed to be a linear approximation of the local phase shifts of modulating line solitons.

Keywords

Cite

@article{arxiv.2307.09932,
  title  = {Linear stability of elastic 2-line solitons for the KP-II equation},
  author = {Tetsu Mizumachi},
  journal= {arXiv preprint arXiv:2307.09932},
  year   = {2023}
}

Comments

To appear in Quarterly of Applied Mathematics