中国物理B ›› 2011, Vol. 20 ›› Issue (11): 110203-110203.doi: 10.1088/1674-1056/20/11/110203

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Constructing infinite sequence exact solutions of nonlinear evolution equations

套格图桑1, 那仁满都拉2   

  1. (1)College of Mathematics, Inner Mongolia University for Nationalities, Tongliao 028043, China; (2)College of Physics and Electronics, Inner Mongolia University for Nationalities, Tongliao 028043, China
  • 收稿日期:2011-05-13 修回日期:2011-06-14 出版日期:2011-11-15 发布日期:2011-11-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 10862003), the Science Research Foundation of Institution of Higher Education of Inner Mongolia Autonomous Region, China (Grant No. NJZZ07031), and the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant No. 2010MS0111).

Constructing infinite sequence exact solutions of nonlinear evolution equations

Taogetusang(套格图桑)a)b)† and Narenmandula(那仁满都拉)c)   

  1. a College of Mathematics, Inner Mongolia University for Nationalities, Tongliao 028043, China; b College of Mathematical Science, Inner Mongolia Normal University, Huhhot 010022, China; c College of Physics and Electronics, Inner Mongolia University for Nationalities, Tongliao 028043, China
  • Received:2011-05-13 Revised:2011-06-14 Online:2011-11-15 Published:2011-11-15
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 10862003), the Science Research Foundation of Institution of Higher Education of Inner Mongolia Autonomous Region, China (Grant No. NJZZ07031), and the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant No. 2010MS0111).

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摘要： To construct the infinite sequence new exact solutions of nonlinear evolution equations and study the first kind of elliptic function, new solutions and the corresponding Bäcklund transformation of the equation are presented. Based on this, the generalized pentavalent KdV equation and the breaking soliton equation are chosen as applicable examples and infinite sequence smooth soliton solutions, infinite sequence peak solitary wave solutions and infinite sequence compact soliton solutions are obtained with the help of symbolic computation system Mathematica. The method is of significance to search for infinite sequence new exact solutions to other nonlinear evolution equations.

关键词: first kind of elliptic function, Bä, cklund transformation, nonlinear evolution equation, new infinite sequence exact solutions

Abstract: To construct the infinite sequence new exact solutions of nonlinear evolution equations and study the first kind of elliptic function, new solutions and the corresponding Bäcklund transformation of the equation are presented. Based on this, the generalized pentavalent KdV equation and the breaking soliton equation are chosen as applicable examples and infinite sequence smooth soliton solutions, infinite sequence peak solitary wave solutions and infinite sequence compact soliton solutions are obtained with the help of symbolic computation system Mathematica. The method is of significance to search for infinite sequence new exact solutions to other nonlinear evolution equations.

Key words: first kind of elliptic function, B?cklund transformation, nonlinear evolution equation, new infinite sequence exact solutions

中图分类号:  (Integrable systems)

  • 02.30.Ik
02.30.Jr (Partial differential equations)