Stability of line solitons for the KP-II equation in R2
著者
書誌事項
Stability of line solitons for the KP-II equation in R2
（Memoirs of the American Mathematical Society, v. 238,
American Mathematical Society, 2015
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注記
Bibliography: p. 93-95
内容説明・目次
内容説明
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.
目次
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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