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The Phase Shift of Line Solitons for the KP-II Equation

  • Tetsu MizumachiEmail author
Chapter
Part of the Fields Institute Communications book series (FIC, volume 83)

Abstract

The KP-II equation was derived by Kadomtsev and Petviashvili (Sov Phys Dokl 15:539–541, 1970) to explain stability of line solitary waves of shallow water. Stability of line solitons has been proved by Mizumachi (Mem AMS 238:1125, 2015; Proc R Soc Edinb Sect A 148:149–198, 2018) and it turns out the local phase shift of modulating line solitons are not uniform in the transverse direction. In this paper, we obtain the L-bound for the local phase shift of modulating line solitons for polynomially localized perturbations.

2010 Mathematics Subject Classification Primary:

35B35 37K40; Secondary 35Q35 

Notes

Acknowledgement

This research is supported by JSPS KAKENHI Grant Number 17K05332.

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Authors and Affiliations

  1. 1.Division of Mathematical and Information SciencesHiroshima UniversityKagamiyama, HiroshimaJapan

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