中国物理B ›› 2003, Vol. 12 ›› Issue (11): 1202-1207.doi: 10.1088/1009-1963/12/11/303

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New doubly periodic and multiple soliton solutions of the generalized (3+1)-dimensional KP equation with variable coefficients

张鸿庆1, 陈怀堂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, Linyi Teachers University, Shandong Linyi 276005, China
  • 收稿日期:2003-02-17 修回日期:2003-05-27 出版日期:2003-11-16 发布日期:2005-03-16
  • 基金资助:
    Project supported by the National Key Basic Research Development Program of China (Grant No 1998030600), and the National Natural Science Foundation of China (Grant No 10072013).

New doubly periodic and multiple soliton solutions of the generalized (3+1)-dimensional KP equation with variable coefficients

Chen Huai-Tang (陈怀堂)ab, Zhang Hong-Qing (张鸿庆)a   

  1. a Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China; b Department of Mathematics, Linyi Teachers University, Shandong Linyi 276005, China
  • Received:2003-02-17 Revised:2003-05-27 Online:2003-11-16 Published:2005-03-16
  • Supported by:
    Project supported by the National Key Basic Research Development Program of China (Grant No 1998030600), and the National Natural Science Foundation of China (Grant No 10072013).

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摘要： A new generalized Jacobi elliptic function method is used to construct the exact travelling wave solutions of nonlinear partial differential equations (PDEs) in a unified way. The main idea of this method is to take full advantage of the elliptic equation which has more new solutions. More new doubly periodic and multiple soliton solutions are obtained for the generalized (3+1)-dimensional Kronig－Penny (KP) equation with variable coefficients. This method can be applied to other equations with variable coefficients.

Abstract: A new generalized Jacobi elliptic function method is used to construct the exact travelling wave solutions of nonlinear partial differential equations (PDEs) in a unified way. The main idea of this method is to take full advantage of the elliptic equation which has more new solutions. More new doubly periodic and multiple soliton solutions are obtained for the generalized (3+1)-dimensional Kronig－Penny (KP) equation with variable coefficients. This method can be applied to other equations with variable coefficients.

Key words: elliptic equation, Jacobi elliptic function, soliton solution

中图分类号:  (Solitons)

  • 05.45.Yv
02.30.Jr (Partial differential equations) 02.60.Lj (Ordinary and partial differential equations; boundary value problems)