%A Zhi Hong-Yan (智红燕), Zhao Xue-Qin (赵雪芹), Zhang Hong-Qing (张鸿庆) %T New expansion algorithm of three Riccati equations and its applications in nonlinear mathematical physics equations %0 Journal Article %D 2005 %J Chin. Phys. B %R 10.1088/1009-1963/14/7/005 %P 1296-1302 %V 14 %N 7 %U {https://cpb.iphy.ac.cn/CN/abstract/article_108104.shtml} %8 2005-06-20 %X 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.