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.
Received: 30 December 2004
Revised: 21 March 2005
Published: 20 June 2005
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
