The Regularized Boussinesq equation: Instability of periodic traveling waves

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:254

Article

Pava, Jaime Angulo¹  Banquet, Carlos²  Silva, Jorge Drumond³  Oliveira, Filipe^4,5 

[1] IME USP, Dept Math, BR-05508090 Sao Paulo, Brazil

[2] Univ Cordoba, Dept Matemat & Estadist, Monteria 76103, Colombia

[3] Inst Super Tecn, Dept Matemat, Ctr Anal Matemat Geometria & Sistemas Dinam LARSy, P-1049001 Lisbon, Portugal

[4] Univ Lisboa CMAF UL, Ctr Matemat & Aplicacoes Fundamentals, Monte De Caparica, Portugal

[5] Univ Nova Lisboa FCT UNL, Fac Ciencias & Tecnol, Monte De Caparica, Portugal

关键词: Linear instability;    Nonlinear instability;    Boussinesq equations;    Coupled Boussinesq equations;    Well-posedness;   

DOI  :  10.1016/j.jde.2013.01.034

来源: Elsevier

【 摘 要 】

In this work we study the linear instability of periodic traveling waves associated with a generalization of the Regularized Boussinesq equation. By using analytic and asymptotic perturbation theory, we establish sufficient conditions for the existence of exponentially growing solutions to the linearized problem and so the linear instability of periodic profiles is obtained. With respect to applications of this approach, we prove the linear/nonlinear instability of cnoidal wave solutions for the modified Regularized Boussinesq equation and for a system of two coupled Boussinesq equations. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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