Date of Original Version

2-2012

Type

Article

Rights Management

Copyright Khayyam Publishing

Abstract or Description

We study asymptotic stability of solitary wave solutions in the one-dimensional Benney--Luke equation, a formally valid approximation for describing two-way water-wave propagation. For this equation, as for the full water-wave problem, the classic variational method for proving orbital stability of solitary waves fails dramatically due to the fact that the second variation of the energy-momentum functional is infinitely indefinite. We establish nonlinear stability in energy norm under the spectral stability hypothesis that the linearization admits no nonzero eigenvalues of nonnegative real part. We then verify this hypothesis for waves of small energy.

Included in

Mathematics Commons

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Published In

Differential and Integral Equations, 26, 3/4, 253-301.