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Chinese Physics, 2006, Vol. 15(10): 2202-2209    DOI: 10.1088/1009-1963/15/10/003
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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.
Keywords:  Jacobi elliptic function method      doubly-periodic solutions      Zakharov--Kuznetsov equation   
Received:  21 November 2005      Revised:  30 May 2006      Accepted manuscript online: 
PACS:  02.30.Jr (Partial differential equations)  
  02.30.Gp (Special functions)  
  02.30.Mv (Approximations and expansions)  
  02.70.Wz (Symbolic computation (computer algebra))  
  05.45.Yv (Solitons)  

Cite this article: 

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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