Stability of line solitons for the KP-II equation in R2 / [electronic resource] Tetsu Mizumachi.

By: Mizumachi, Tetsu, 1969-Material type: TextTextSeries: Memoirs of the American Mathematical Society ; v. 1125Publisher: Providence, Rhode Island : American Mathematical Society, 2015Description: 1 online resource (pages cm.)Content type: text Media type: unmediated Carrier type: volumeISBN: 9781470426132 (online)Subject(s): Solitons | Wave-motion, Theory of | Symmetry (Mathematics) | Representations of algebrasAdditional physical formats: Stability of line solitons for the KP-II equation in R2 /DDC classification: 530.12/4 LOC classification: QC174.26.W28 | M59 2015Online resources: Contents | Contents
Contents:
Acknowledgments Chapter 1. Introduction Chapter 2. The Miura transformation and resonant modes of the linearized operator Chapter 3. Semigroup estimates for the linearized KP-II equation Chapter 4. Preliminaries Chapter 5. Decomposition of the perturbed line soliton Chapter 6. Modulation equations Chapter 7. A priori estimates for the local speed and the local phase shift Chapter 8. The $L^2(\mathbb {R}^2)$ estimate Chapter 9. Decay estimates in the exponentially weighted space Chapter 10. Proof of Theorem 1.1 Chapter 11. Proof of Theorem 1.4 Chapter 12. Proof of Theorem 1.5 Appendix A. Proof of Lemma 6.1 Appendix B. Operator norms of $S^j_k$ and $\protect \widetilde {C_k}$ 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
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Includes bibliographical references.

Acknowledgments Chapter 1. Introduction Chapter 2. The Miura transformation and resonant modes of the linearized operator Chapter 3. Semigroup estimates for the linearized KP-II equation Chapter 4. Preliminaries Chapter 5. Decomposition of the perturbed line soliton Chapter 6. Modulation equations Chapter 7. A priori estimates for the local speed and the local phase shift Chapter 8. The $L^2(\mathbb {R}^2)$ estimate Chapter 9. Decay estimates in the exponentially weighted space Chapter 10. Proof of Theorem 1.1 Chapter 11. Proof of Theorem 1.4 Chapter 12. Proof of Theorem 1.5 Appendix A. Proof of Lemma 6.1 Appendix B. Operator norms of $S^j_k$ and $\protect \widetilde {C_k}$ 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

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Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2015

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