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Showing 1 to 3 of 3 for “"Whitham equation"”.
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Spectral stability of solutions to Whitham-type equations with a nonlocal kernel
… to certain nonlinear partial differential equations. This is done using a spectral cosine collocation method, and the stability of the travelling wave solutions found is then assessed using the Fourier-Floquet-Hill method. This is first done on a number of examples. Next, a variation of the …
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On Steady Water Waves and Their Properties
… trajectories. Paper IV: Travelling waves for the Whitham equation. The existence of travelling waves for the original Whitham equation is investigated. This equation combines a generic nonlinear quadratic term with the exact linear dispersion relation of surface water waves on finite depth. It is …
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Modulational instability in some shallow water wave models
… like Benjamin-Bona-Mahony and Camassa-Holm equations. We propose a bi-directional shallow water model which generalizes Whitham equation to contain the nonlinearities of nonlinear shallow water equations. The analysis yields a modulational instability index for each model which is solely …