English

The phase shift of line solitons for the KP-II equation

Analysis of PDEs 2018-08-03 v1 Mathematical Physics math.MP

Abstract

The KP-II equation was derived by [B. B. Kadomtsev and V. I. Petviashvili,Sov. Phys. Dokl. vol.15 (1970), 539-541] to explain stability of line solitary waves of shallow water. Stability of line solitons has been proved by [T. Mizumachi, Mem. of vol. 238 (2015), no.1125] and [T. Mizumachi, Proc. Roy. Soc. Edinburgh Sect. A. vol.148 (2018), 149--198]. It turns out the local phase shift of modulating line solitons are not uniform in the transverse direction. In this paper, we obtain the LL^\infty-bound for the local phase shift of modulating line solitons for polynomially localized perturbations.

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Cite

@article{arxiv.1808.00809,
  title  = {The phase shift of line solitons for the KP-II equation},
  author = {Tetsu Mizumachi},
  journal= {arXiv preprint arXiv:1808.00809},
  year   = {2018}
}