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- W4289743107 abstract "We study the existence of traveling wave solutions to a unidirectional shallow water model which incorporates the full linear dispersion relation for both gravitational and capillary restoring forces. Using functional analytic techniques, we show that for small surface tension (corresponding to Bond numbers between $0$ and ${1}/{3}$) there exists small amplitude solitary waves that decay to asymptotically small periodic waves at spatial infinity. The size of the oscillations in the far field are shown to be small beyond all algebraic orders in the amplitude of the wave. We also present numerical evidence, based on the recent analytical work of Hur & Johnson, that the asymptotic end states are modulationally stable for all Bond numbers between $0$ and $1/3$." @default.
- W4289743107 created "2022-08-04" @default.
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- W4289743107 date "2018-07-30" @default.
- W4289743107 modified "2023-10-18" @default.
- W4289743107 title "Generalized Solitary Waves in the Gravity-Capillary Whitham Equation" @default.
- W4289743107 doi "https://doi.org/10.48550/arxiv.1807.11469" @default.
- W4289743107 hasPublicationYear "2018" @default.
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