We review some results on asymptotic stability of nonlinear waves for a few dispersive or wave models, like the nonlinear Schrödinger equation, the generalized Korteweg-de Vries equation, and the nonlinear wave and Klein-Gordon equations. Then, we focus on recent results of the authors concerning the asymptotic stability of the kink for the equation under odd perturbations. We also present two results (one of which seems previously unknown) of non-existence of small breathers for some nonlinear Klein-Gordon equations.
@article{SLSEDP_2016-2017____A18_0, author = {Micha{\l} Kowalczyk and Yvan Martel and Claudio Mu\~noz}, title = {On asymptotic stability of nonlinear waves}, journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications}, note = {talk:18}, pages = {1--27}, publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique}, year = {2016-2017}, doi = {10.5802/slsedp.111}, language = {en}, url = {https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.111/} }
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Michał Kowalczyk; Yvan Martel; Claudio Muñoz. On asymptotic stability of nonlinear waves. Séminaire Laurent Schwartz — EDP et applications (2016-2017), Talk no. 18, 27 p. doi : 10.5802/slsedp.111. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.111/
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