Model Equations for Three-Dimensional Nonlinear Water Waves under Tangential Electric Field
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 u...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2017/9312681 |
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| author | Bo Tao |
| author_facet | Bo Tao |
| author_sort | Bo Tao |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b27af2a0b6bc4181ae4b980d0e2fe22b |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-b27af2a0b6bc4181ae4b980d0e2fe22b2025-02-03T05:45:46ZengWileyAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/93126819312681Model Equations for Three-Dimensional Nonlinear Water Waves under Tangential Electric FieldBo Tao0School of Architecture Engineering, Neijiang Normal University, Sichuan 641100, ChinaWe 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.http://dx.doi.org/10.1155/2017/9312681 |
| spellingShingle | Bo Tao Model Equations for Three-Dimensional Nonlinear Water Waves under Tangential Electric Field Advances in Mathematical Physics |
| title | Model Equations for Three-Dimensional Nonlinear Water Waves under Tangential Electric Field |
| title_full | Model Equations for Three-Dimensional Nonlinear Water Waves under Tangential Electric Field |
| title_fullStr | Model Equations for Three-Dimensional Nonlinear Water Waves under Tangential Electric Field |
| title_full_unstemmed | Model Equations for Three-Dimensional Nonlinear Water Waves under Tangential Electric Field |
| title_short | Model Equations for Three-Dimensional Nonlinear Water Waves under Tangential Electric Field |
| title_sort | model equations for three dimensional nonlinear water waves under tangential electric field |
| url | http://dx.doi.org/10.1155/2017/9312681 |
| work_keys_str_mv | AT botao modelequationsforthreedimensionalnonlinearwaterwavesundertangentialelectricfield |