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

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  • Bo Tao

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.

Suggested Citation

  • Bo Tao, 2017. "Model Equations for Three-Dimensional Nonlinear Water Waves under Tangential Electric Field," Advances in Mathematical Physics, Hindawi, vol. 2017, pages 1-8, November.
    • Handle: RePEc:hin:jnlamp:9312681
    DOI: 10.1155/2017/9312681
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