Stability of Line Solitons for the KP-II Equation in R²
Author:   Tetsu Mizumachi
Publisher:   American Mathematical Society
ISBN:  

9781470414245


Pages:   95
Publication Date:   30 December 2015
Format:   Paperback
Availability:   Temporarily unavailable   Availability explained
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Stability of Line Solitons for the KP-II Equation in R²


Overview

The author proves nonlinear stability of line soliton solutions of the KP-II equation with respect to transverse perturbations that are exponentially localized as $x\to\infty$. He finds that the amplitude of the line soliton converges to that of the line soliton at initial time whereas jumps of the local phase shift of the crest propagate in a finite speed toward $y=\pm\infty$. The local amplitude and the phase shift of the crest of the line solitons are described by a system of 1D wave equations with diffraction terms.

Full Product Details

Author:   Tetsu Mizumachi
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Weight:   0.280kg
ISBN:  

9781470414245


ISBN 10:   1470414244
Pages:   95
Publication Date:   30 December 2015
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Temporarily unavailable   Availability explained
The supplier advises that this item is temporarily unavailable. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out to you.

Table of Contents

Introduction The Miura transformation and resonant modes of the linearized operator Semigroup estimates for the linearized KP-II equation Preliminaries Decomposition of the perturbed line soliton Modulation equations A priori estimates for the local speed and the local phase shift The $L^2(\mathbb{R}^2)$ estimate Decay estimates in the exponentially weighted space Proof of Theorem 1.1 Proof of Theorem 1.4 Proof of Theorem 1.5 Appendix A. Proof of Lemma 6.1 Appendix B. Operator norms of $S^j_k$ and $\widetilde{C_k}$ Appendix C. Proofs of Claims 6.2, 6.3 and 7.1 Appendix D. Estimates of $R^k$ Appendix E. Local well-posedness in exponentially weighted space Bibliography

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Author Information

Tetsu Mizumachi, Kyushu University, Fukuoka, Japan.

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