中国物理B ›› 2004, Vol. 13 ›› Issue (1): 1-4.doi: 10.1088/1009-1963/13/1/001

• GENERAL •    下一篇

Backlünd transformation and multiple soliton solutions for the (3+1)-dimensional Nizhnik－Novikov－Veselov equation

白成林   

  1. Department of Communication Engineering, Liaocheng University, Liaocheng 252059, China
  • 收稿日期:2003-02-26 修回日期:2003-06-25 出版日期:2005-01-22 发布日期:2007-03-22
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 60177009), and the Natural Science Foundation of Shandong Province, China (Grant No Q2003G07).

Backlünd transformation and multiple soliton solutions for the (3+1)-dimensional Nizhnik－Novikov－Veselov equation

Bai Cheng-Lin (白成林)   

  1. Department of Communication Engineering, Liaocheng University, Liaocheng 252059, China
  • Received:2003-02-26 Revised:2003-06-25 Online:2005-01-22 Published:2007-03-22
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 60177009), and the Natural Science Foundation of Shandong Province, China (Grant No Q2003G07).

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摘要： We develop an approach to construct multiple soliton solutions of the (3+1)-dimensional nonlinear evolution equation. We take the (3+1)-dimensional Nizhnik－Novikov－Veselov (NNV) equation as an example. Using the extended homogeneous balance method, one can find a Backlünd transformation to decompose the (3+1)-dimensional NNV into a set of partial differential equations. Starting from these partial differential equations, some multiple soliton solutions for the (3+1)-dimensional NNV equation are obtained by introducing a class of formal solutions.

Abstract: We develop an approach to construct multiple soliton solutions of the (3+1)-dimensional nonlinear evolution equation. We take the (3+1)-dimensional Nizhnik－Novikov－Veselov (NNV) equation as an example. Using the extended homogeneous balance method, one can find a Backlünd transformation to decompose the (3+1)-dimensional NNV into a set of partial differential equations. Starting from these partial differential equations, some multiple soliton solutions for the (3+1)-dimensional NNV equation are obtained by introducing a class of formal solutions.

Key words: soliton, extended homogeneous balance method, (3+1)-dimensional NNV equation

中图分类号:  (Ordinary differential equations)

  • 02.30.Hq
02.30.Jr (Partial differential equations) 02.60.Cb (Numerical simulation; solution of equations)