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

Häftad, Engelska, 2015

1 219 kr

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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.

Produktinformation

Utgivningsdatum2015-11-01
Mått178 x 254 x undefined mm
Vikt280 g
FormatHäftad
SpråkEngelska
SerieMemoirs of the American Mathematical Society
FörlagAmerican Mathematical Society
ISBN9781470414245

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Beräkning och matematisk analys inom Naturvetenskap och teknik

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