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Stability of line solitons for the KP-II equation in ℝ2. II

Published online by Cambridge University Press:  20 September 2017

Tetsu Mizumachi*
Affiliation:
Division of Mathematical and Information Sciences, Hiroshima University, 1-7-1 Kagamiyama 739-8521, Japan (tetsum@hiroshima-u.ac.jp)

Abstract

The KP-II equation was derived by Kadmotsev and Petviashvili to explain stability of line solitary waves of shallow water. Recently, Mizumachi proved nonlinear stability of 1-line solitons for exponentially localized perturbations. In this paper, we prove stability of 1-line solitons for perturbations in (1 + x2)1/20H1(ℝ2) and perturbations in H1(ℝ2) ∩ ∂xL2(ℝ2).

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2018 

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