中国物理B ›› 2006, Vol. 15 ›› Issue (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

智红燕1, 张鸿庆1, 赵雪芹2   

  1. (1)Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China; (2)Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China ;Department of Mathematics, Qufu Normal University, Qufu 273165, China
  • 收稿日期:2005-11-21 修回日期:2006-05-30 出版日期:2006-10-20 发布日期:2006-10-20

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)   

  1. a Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China; b Department of Mathematics, Qufu Normal University, Qufu 273165, China
  • Received:2005-11-21 Revised:2006-05-30 Online:2006-10-20 Published:2006-10-20

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摘要： 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.

关键词: Jacobi elliptic function method, doubly-periodic solutions, Zakharov--Kuznetsov equation

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.

Key words: Jacobi elliptic function method, doubly-periodic solutions, Zakharov--Kuznetsov equation

中图分类号:  (Partial differential equations)

  • 02.30.Jr
02.30.Gp (Special functions) 02.30.Mv (Approximations and expansions) 02.70.Wz (Symbolic computation (computer algebra)) 05.45.Yv (Solitons)