# Stability of Line Solitons for the KP-II Equation in \(\mathbb {R}^2\)

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*Tetsu Mizumachi*

#### Table of Contents

# Table of Contents

## Stability of Line Solitons for the KP-II Equation in $\mathbb{R}^{2}$

- Cover Cover11 free
- Title page i2 free
- Acknowledgments vii8 free
- Chapter 1. Introduction 110 free
- Chapter 2. The Miura transformation and resonant modes of the linearized operator 716 free
- Chapter 3. Semigroup estimates for the linearized KP-II equation 1928
- Chapter 4. Preliminaries 2736
- Chapter 5. Decomposition of the perturbed line soliton 3140
- Chapter 6. Modulation equations 3746
- Chapter 7. ร priori estimates for the local speed and the local phase shift 4554
- Chapter 8. The ๐ฟยฒ(\Rยฒ) estimate 5362
- Chapter 9. Decay estimates in the exponentially weighted space 5766
- Chapter 10. Proof of Theorem 1.1 6372
- Chapter 11. Proof of Theorem 1.4 6574
- Chapter 12. Proof of Theorem 1.5 6978
- Appendix A. Proof of Lemma 6.1 7786
- Appendix B. Operator norms of ๐^{๐}_{๐} and ฬ๐ถ_{๐} 7988
- Appendix C. Proofs of Claims 6.2, 6.3 and 7.1 8392
- Appendix D. Estimates of ๐ ^{๐} 8594
- Appendix E. Local well-posedness in exponentially weighted space 91100
- Bibliography 93102
- Back Cover Back Cover1110