On the stability of periodic solutions of the generalized Benjamin-Bona-Mahony equation

PHYSICA D-NONLINEAR PHENOMENA

卷:239

Article

Johnson, Mathew A.

关键词: Generalized Benjamin-Bona-Mahony equation;    Periodic waves;    Modulational instability;    Nonlinear stability;   

DOI  :  10.1016/j.physd.2010.06.011

来源: Elsevier

【 摘 要 】

We study the stability of a four-parameter family of spatially periodic traveling wave solutions of the generalized Benjamin-Bona-Mahony equation under two classes of perturbations: periodic perturbations with the same periodic structure as the underlying wave, and long wavelength localized perturbations. In particular, we derive necessary conditions for spectral instability under perturbation for both classes of perturbations by deriving appropriate asymptotic expansions of the periodic Evans function, and we outline a theory of nonlinear stability under periodic perturbations based on variational methods which effectively extends our periodic spectral stability results. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

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