Model Equations for Three-Dimensional Nonlinear Water Waves under Tangential Electric Field

Bo Tao

Advances in Mathematical Physics, 2017, vol. 2017, 1-8

Abstract:

We are concerned with gravity-capillary waves propagating on the surface of a three-dimensional electrified liquid sheet under a uniform electric field parallel to the undisturbed free surface. For simplicity, we make an assumption that the permittivity of the fluid is much larger than that of the upper-layer gas; hence, this two-layer problem is reduced to be a one-layer problem. In this paper, we propose model equations in the shallow-water regime based on the analysis of the Dirichlet-Neumann operator. The modified Benney-Luke equation and Kadomtsev-Petviashvili equation will be derived, and the truly three-dimensional fully localized traveling waves, which are known as “lumps” in the literature, are numerically computed in the Benney-Luke equation.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:9312681

DOI: 10.1155/2017/9312681

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