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A quasi-one-dimensional asymptotic theory for non-linear water waves

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Abstract

Quasi-one-dimensional generalizations of different forms of the one-dimensional Boussinesq equations are derived asymptotically, then, from these quasi-one-dimentional Boussineq equations, a consistent and significant second-order KP equation is derived, according to the Kadomtsev-Petviashvili [1] limiting process, the asymptotic expansions in the derivation of the non-linear Schrödinger-Poisson (NLSP) system of two equations, obtained by Freeman and Davey [2], in the long-water-waves limit are also determined.

Finally, I elucidate the influence of a bottom topography on the Boussinesq and KP equations.

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  1. Université de Lille I, L.M.L., C.N.R.S.-U.R.A. 1441, 59655, Villeneuve d'Ascq, Cédex, France

    R. Kh. Zeytounian

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Zeytounian, R.K. A quasi-one-dimensional asymptotic theory for non-linear water waves. J Eng Math 28, 261–296 (1994). https://doi.org/10.1007/BF00128748

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