Construction of doubly-periodic solutions to nonlinear partial differential equations using improved Jacobi elliptic function expansion method and symbolic computation
Zhao Xue-Qin(赵雪芹)a)b)†, Zhi Hong-Yan(智红燕)a), and Zhang Hong-Qing(张鸿庆)a)
a Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China; b Department of Mathematics, Qufu Normal University, Qufu 273165, China
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 function solutions to construct doubly-periodic solutions of the Zakharov--Kuznetsov equation, which has been derived by Gottwald as a two-dimensional model for nonlinear Rossby waves. When the modulus $k \rightarrow 1$, these solutions reduce to the solitary wave solutions of the equation.
Received: 21 November 2005
Revised: 30 May 2006
Accepted manuscript online:
Zhao Xue-Qin(赵雪芹), Zhi Hong-Yan(智红燕), and Zhang Hong-Qing(张鸿庆) Construction of doubly-periodic solutions to nonlinear partial differential equations using improved Jacobi elliptic function expansion method and symbolic computation 2006 Chinese Physics 15 2202
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