Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1897355 | Physica D: Nonlinear Phenomena | 2010 | 17 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Mathew A. Johnson,