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Water Wave Packets Over Variable Depth
Author(s) -
Grimshaw R. H. J.,
Annenkov S. Y.
Publication year - 2011
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2010.00508.x
Subject(s) - variable (mathematics) , wave packet , network packet , physics , mathematics , geology , mathematical analysis , computer science , quantum mechanics , computer network
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.