Stability for the modified and fourth-order Benjamin-Bona-Mahony equations

Jaime Angulo Pava; Carlos Banquet; Márcia Scialom

doi:10.3934/dcds.2011.30.851

Article Contents

2011, Volume 30, Issue 3: 851-871. Doi: 10.3934/dcds.2011.30.851

This issue Previous Article Frequency locking of modulated waves Next Article On uniform convergence in ergodic theorems for a class of skew product transformations

Stability for the modified and fourth-order Benjamin-Bona-Mahony equations

1.
Department of Mathematics, IME-USP, Rua do Matão 1010, Cidade Universitária, CEP 05508-090, São Paulo, SP
2.
Department of Mathematics, IMECC-UNICAMP, Rua Sérgio Buarque de Holanda 651, CEP 13083-859, Campinas, SP

Received: October 31, 2009

Revised: November 30, 2010

Published: August 2011

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Abstract

In this work we establish new results about the existence of smooth, explicit families of periodic traveling waves for the modified and fourth-order Benjamin-Bona-Mahony equations. We also prove, under certain conditions, that these families are nonlinearly stable in the energy space. The techniques employed may be of further use in the study of the stability of periodic traveling-wave solutions of other nonlinear evolution equations.

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Mathematics Subject Classification: Primary: 35Q53; Secondary: 35B35, 35B10.

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