中国物理B ›› 2009, Vol. 18 ›› Issue (2): 475-481.doi: 10.1088/1674-1056/18/2/017

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Some new solutions derived from the nonlinear (2+1)-dimensional Toda equation---an efficient method of creating solutions

张立华1, 白成林2, 张霞2   

  1. (1)Department of Mathematics, Dezhou College, Dezhou 253023, China; (2)School of Physics Science and Information Engineering, Liaocheng University, Liaocheng 252059, China
  • 收稿日期:2008-06-22 修回日期:2008-07-17 出版日期:2009-02-20 发布日期:2009-02-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China and the Natural Science Foundation of Shandong Province in China (Grant No Y2007G64).

Some new solutions derived from the nonlinear (2+1)-dimensional Toda equation---an efficient method of creating solutions

Bai Cheng-Lin(白成林)a)†, Zhang Xia(张霞)a), and Zhang Li-Hua (张立华)b)   

  1. a School of Physics Science and Information Engineering, Liaocheng University, Liaocheng 252059, China; b Department of Mathematics, Dezhou College, Dezhou 253023, China
  • Received:2008-06-22 Revised:2008-07-17 Online:2009-02-20 Published:2009-02-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China and the Natural Science Foundation of Shandong Province in China (Grant No Y2007G64).

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摘要： This paper presents a new and efficient approach for constructing exact solutions to nonlinear differential--difference equations (NLDDEs) and lattice equation. By using this method via symbolic computation system MAPLE, we obtained abundant soliton-like and/or period-form solutions to the (2+1)-dimensional Toda equation. It seems that solitary wave solutions are merely special cases in one family. Furthermore, the method can also be applied to other nonlinear differential--difference equations.

关键词: hyperbolic function method, nonlinear differential--difference equations, soliton-like solutions, period-form solutions

Abstract: This paper presents a new and efficient approach for constructing exact solutions to nonlinear differential--difference equations (NLDDEs) and lattice equation. By using this method via symbolic computation system MAPLE, we obtained abundant soliton-like and/or period-form solutions to the (2+1)-dimensional Toda equation. It seems that solitary wave solutions are merely special cases in one family. Furthermore, the method can also be applied to other nonlinear differential--difference equations.

Key words: hyperbolic function method, nonlinear differential--difference equations, soliton-like solutions, period-form solutions

中图分类号:  (Lattice theory and statistics)

  • 05.50.+q
05.45.Yv (Solitons) 02.30.Jr (Partial differential equations)