[Asymptotic stability of solitary waves for the Benjamin–Bona–Mahony equation]
We prove the asymptotic stability in of the family of solitary waves for the Benjamin–Bona–Mahony equation. The proof is based on a Liouville type theorem on the flow around the solitary waves.
Nous montrons la stabilité asymptotique dans de la famille des ondes solitaires de l'équation de Benjamin–Bona–Mahony. Nous obtenons ce résultat en montrant un théorème de rigidité du flot autour des ondes solitaires (un théorème de type Liouville).
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Khaled El Dika 1
@article{CRMATH_2003__337_10_649_0, author = {Khaled El Dika}, title = {Stabilit\'e asymptotique des ondes solitaires de l'\'equation de {Benjamin{\textendash}Bona{\textendash}Mahony}}, journal = {Comptes Rendus. Math\'ematique}, pages = {649--652}, publisher = {Elsevier}, volume = {337}, number = {10}, year = {2003}, doi = {10.1016/j.crma.2003.10.003}, language = {fr}, }
Khaled El Dika. Stabilité asymptotique des ondes solitaires de l'équation de Benjamin–Bona–Mahony. Comptes Rendus. Mathématique, Volume 337 (2003) no. 10, pp. 649-652. doi : 10.1016/j.crma.2003.10.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.10.003/
[1] Model equations for long waves in nonlinear dispersive systems, Philos. Trans. Roy. Soc. London Ser. A, Volume 272 (1972) no. 1220, pp. 47-78
[2] On the stability of solitary-waves solutions of model equations for long waves, J. Nonlinear Sci., Volume 4 (1994) no. 5, pp. 449-470
[3] K. El Dika, Asymptotic stability of solitary waves for the Benjamin–Bona–Mahony equation, en préparation
[4] A Liouville theorem for the critical generalized Korteweg–de Vries equation, J. Math. Pures Appl. (9), Volume 79 (2000) no. 4, pp. 339-425
[5] Asymptotic stability of solitons for subcritical generalized KdV equations, Arch. Rational Mech. Anal., Volume 157 (2001) no. 3, pp. 219-254
[6] Asymptotic stability of solitary waves for the regularized long-wave equation, Comm. Pure Appl. Math., Volume 49 (1996) no. 4, pp. 399-441
[7] Existence and dynamic stability of solitary wave solutions of equations arising in long wave propagation, Comm. Partial Differential Equations, Volume 12 (1987) no. 10, pp. 1133-1173
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