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• W1836201842 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." @default.
• W1836201842 created "2016-06-24" @default.
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• W1836201842 date "2013-03-01" @default.
• W1836201842 modified "2023-10-12" @default.
• W1836201842 title "Asymptotic stability of solitary waves in the Benney-Luke model of water waves" @default.
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• W1836201842 doi "https://doi.org/10.57262/die/1360092825" @default.
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