Asymptotic stability of solitary waves in the Benney-Luke model of water waves

Details Asymptotic stability of solitary waves in the Benney-Luke model of water waves Asymptotic stability of solitary waves in the Benney-Luke model of water waves

2012-02-02

arxiv.org/abs/1202.0450v1

Nonlinear Sciences

Pattern Formation and Solitons

40 pages, LaTeX with amsmath, amsfonts, amssymb, amsaddr packages

Scientific paper

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 non-zero eigenvalues of non-negative real part. We also verify this hypothesis for waves of small energy.

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