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Chin. Phys., 2005, Vol. 14(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

Zhi Hong-Yana, Zhang Hong-Qinga, Zhao Xue-Qinb
a Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China;; b Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China;Department of Mathematics, Qufu Normal University, Qufu 273165, China
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\"{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.
Keywords:  higher-order Schr\"{o}dinger equation      solitary wave solution      periodic solution      symbolic computation      mKdV equation  
Received:  30 December 2004      Revised:  21 March 2005      Published:  20 June 2005
PACS:  03.65.Ge (Solutions of wave equations: bound states)  
  05.45.Yv (Solitons)  
  02.30.-f (Function theory, analysis)  

Cite this article: 

Zhi Hong-Yan, Zhao Xue-Qin, Zhang Hong-Qing New expansion algorithm of three Riccati equations and its applications in nonlinear mathematical physics equations 2005 Chin. Phys. 14 1296

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