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March/April 2013 Asymptotic stability of solitary waves in the Benney-Luke model of water waves
Tetsu Mizumachi, Robert L. Pego, José Raúl Quintero
Differential Integral Equations 26(3/4): 253-301 (March/April 2013).

Abstract

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.

Citation

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Tetsu Mizumachi. Robert L. Pego. José Raúl Quintero. "Asymptotic stability of solitary waves in the Benney-Luke model of water waves." Differential Integral Equations 26 (3/4) 253 - 301, March/April 2013.

Information

Published: March/April 2013
First available in Project Euclid: 5 February 2013

zbMATH: 1289.37043
MathSciNet: MR3059165

Subjects:
Primary: 35B35, 35Q35, 37K40, 76B15

Rights: Copyright © 2013 Khayyam Publishing, Inc.

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Vol.26 • No. 3/4 • March/April 2013
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