Construction of doubly-periodic solutions to nonlinear partial differential equations using improved Jacobi elliptic function expansion method and symbolic computation |
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| Authors: | Zhao Xue-Qin Zhi Hong-Yan Zhang Hong-Qing |
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| Affiliation: | Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China; Department of Mathematics, Qufu Normal University, Qufu 273165, China |
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| Abstract: | Some doubly-periodic solutions of the Zakharov--Kuznetsov equation are presented. Our approach is to introduce an auxiliary ordinary differential equation and use its Jacobi elliptic functionsolutions to construct doubly-periodic solutions of the Zakharov--Kuznetsovequation, which has been derived by Gottwald as a two-dimensional model fornonlinear Rossby waves. When the modulus k rightarrow 1, these solutions reduceto the solitary wave solutions of the equation. |
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| Keywords: | Jacobi elliptic function method doubly-periodic solutions Zakharov--Kuznetsov equation |
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