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

Part of: Equations of mathematical physics and other areas of application Partial differential equations Infinite-dimensional Hamiltonian systems

Published online by Cambridge University Press:  20 September 2017

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

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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)−1/2−0H1(ℝ2) and perturbations in H1(ℝ2) ∩ ∂xL2(ℝ2).

Keywords

KP-IIline solitontransverse stability

MSC classification

Secondary: 35B35: Stability 37K40: Soliton theory, asymptotic behavior of solutions 35Q53: KdV-like equations (Korteweg-de Vries) 37K45: Stability problems
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 148 , Issue 1 , February 2018 , pp. 149 - 198
Copyright
Copyright © Royal Society of Edinburgh 2018