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

Bo Tao

Advances in Mathematical Physics, 2017, vol. 2017, issue 1

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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https://doi.org/10.1155/2017/9312681

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2017:y:2017:i:1:n:9312681

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