中国物理B ›› 2005, Vol. 14 ›› Issue (7): 1296-1302.doi: 10.1088/1009-1963/14/7/005

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New expansion algorithm of three Riccati equations and its applications in nonlinear mathematical physics equations

智红燕1, 张鸿庆1, 赵雪芹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, Qufu Normal University, Qufu 273165, China
  • 收稿日期:2004-12-30 修回日期:2005-03-21 出版日期:2005-06-20 发布日期:2005-06-20

New expansion algorithm of three Riccati equations and its applications in nonlinear mathematical physics equations

Zhi Hong-Yan (智红燕)a, Zhao Xue-Qin (赵雪芹)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, Qufu Normal University, Qufu 273165, China
  • Received:2004-12-30 Revised:2005-03-21 Online:2005-06-20 Published:2005-06-20

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摘要： Based on the study of tanh function method and the coupled projective Riccati equation method, we propose a new algorithm to search for explicit exact solutions of nonlinear evolution equations. We use the higher-order Schr\"{o}dinger equation and mKdV equation to illustrate this algorithm. As a result, more new solutions are obtained, which include new solitary solutions, periodic solutions, and singular solutions.Some new solutions are illustrated in figures.

关键词: symbolic computation, solitary wave solution, periodic solution, higher-order Schr\"{o}dinger equation, mKdV equation

Abstract: Based on the study of tanh function method and the coupled projective Riccati equation method, we propose a new algorithm to search for explicit exact solutions of nonlinear evolution equations. We use the higher-order Schr$\ddot{\rm o}$dinger equation and mKdV equation to illustrate this algorithm. As a result, more new solutions are obtained, which include new solitary solutions, periodic solutions, and singular solutions.Some new solutions are illustrated in figures.

Key words: symbolic computation, solitary wave solution, periodic solution, higher-order Schr$\ddot{\rm o}$dinger equation, mKdV equation

中图分类号:  (Solutions of wave equations: bound states)

  • 03.65.Ge
05.45.Yv (Solitons) 02.30.-f (Function theory, analysis)