Stability of Line Solitons for the KP-II Equation in R²

Tetsu Mizumachi, Kyushu University, Fukuoka, Japan.

• IntroductionThe Miura transformation and resonant modes of the linearized operatorSemigroup estimates for the linearized KP-II equationPreliminariesDecomposition of the perturbed line solitonModulation equationsA priori estimates for the local speed and the local phase shiftThe $L^2(\mathbb{R}^2)$ estimateDecay estimates in the exponentially weighted spaceProof of Theorem 1.1Proof of Theorem 1.4Proof of Theorem 1.5Appendix A. Proof of Lemma 6.1Appendix B. Operator norms of $S^j_k$ and $\widetilde{C_k}$Appendix C. Proofs of Claims 6.2, 6.3 and 7.1Appendix D. Estimates of $R^k$Appendix E. Local well-posedness in exponentially weighted spaceBibliography