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Water Wave Packets Over Variable Depth

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In this paper, we develop higher-order nonlinear Schrödinger equations with variable coefficients to describe how a water wave packet will deform and eventually be destroyed as it propagates shoreward from deep to shallow water. It is well-known that in the framework of the usual nonlinear Schrödinger equations, a wave packet can only exist in deep water, more precisely when  kh > 1.363 , where  k  is the wavenumber and  h  is the depth. Using a combination of asymptotic analysis and numerical simulations we find that in the framework of the higher-order nonlinear Schrödinger equations, the wave packet can penetrate into shallow water  kh < 1.363  or not even reach  kh > 1.363 , depending on the sign of the initial value in deep water of a certain parameter of the wave packet that measures its speed.
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Document Type: Research Article

Affiliations: Loughborough University

Publication date: May 1, 2011

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