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- W4301239344 abstract "We propose a shallow water model which combines the dispersion relation of water waves and the Boussinesq equations, and which extends the Whitham equation to permit bidirectional propagation. We establish that its sufficiently small, periodic wave train is spectrally unstable to long wavelength perturbations, provided that the wave number is greater than a critical value, like the Benjamin-Feir instability of a Stokes wave. We verify that the asso- ciated linear operator possesses infinitely many collisions of purely imaginary eigenvalues, but they do not contribute to instability away from the origin in the spectral plane to the leading order in the amplitude parameter. We discuss the effects of surface tension on the modulational instability. The results agree with those from formal asymptotic expansions and numerical computations for the physical problem." @default.
- W4301239344 created "2022-10-05" @default.
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- W4301239344 date "2016-08-16" @default.
- W4301239344 modified "2023-09-28" @default.
- W4301239344 title "Modulational instability in a full-dispersion shallow water model" @default.
- W4301239344 doi "https://doi.org/10.48550/arxiv.1608.04685" @default.
- W4301239344 hasPublicationYear "2016" @default.
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