中国物理B ›› 2002, Vol. 11 ›› Issue (5): 425-428.doi: 10.1088/1009-1963/11/5/303

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B?cklund transformation and multiple soliton solutions for the (3+1)-dimensional Jimbo-Miwa equation

张解放, 吴锋民   

  1. Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua 321004, China
  • 收稿日期:2001-09-13 修回日期:2001-12-20 出版日期:2002-05-13 发布日期:2005-06-13
  • 基金资助:
    Project supported by the Natural Science Foundation of Zhejiang Province, China (Grant No 100039).

Bäcklund transformation and multiple soliton solutions for the (3+1)-dimensional Jimbo-Miwa equation

Zhang Jie-Fang (张解放), Wu Feng-Min (吴锋民)   

  1. Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua 321004, China
  • Received:2001-09-13 Revised:2001-12-20 Online:2002-05-13 Published:2005-06-13
  • Supported by:
    Project supported by the Natural Science Foundation of Zhejiang Province, China (Grant No 100039).

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摘要： We study an approach to constructing multiple soliton solutions of the (3+1)-dimensional nonlinear evolution equation. We take the (3+1)-dimensional Jimbo－Miwa (JM) equation as an example. Using the extended homogeneous balance method, one can find a B?cklund transformation to decompose the (3+1)-dimensional JM equation into a linear partial differential equation and two bilinear partial differential equations. Starting from these linear and bilinear partial differential equations, some multiple soliton solutions for the (3+1)-dimensional JM equation are obtained by introducing a class of formal solutions.

Abstract: We study an approach to constructing multiple soliton solutions of the (3+1)-dimensional nonlinear evolution equation. We take the (3+1)-dimensional Jimbo－Miwa (JM) equation as an example. Using the extended homogeneous balance method, one can find a B?cklund transformation to decompose the (3+1)-dimensional JM equation into a linear partial differential equation and two bilinear partial differential equations. Starting from these linear and bilinear partial differential equations, some multiple soliton solutions for the (3+1)-dimensional JM equation are obtained by introducing a class of formal solutions.

Key words: soliton, homogeneous balance method, (3+1)-dimensions, JM equation

中图分类号:  (Partial differential equations)

  • 02.30.Jr