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line soliton

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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Stability of line solitons for the KP-II equation in ℝ2. II
Part of
Tetsu Mizumachi
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 148 / Issue 1 / February 2018

Published online by Cambridge University Press:

20 September 2017, pp. 149-198

Print publication:

February 2018
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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).