Variable-coefficient projective Riccati equation method and its application to a new (2 + 1)-dimensional simplified generalized Broer-Kaup system
The paper is concerned with the projective Riccati equation method proposed by \textit{R. Conte} and \textit{M. Musette} [J. Phys. A, Math. Gen. 25, No. 21, 5609--5623 (1992; Zbl 0782.35065)] to seek new solitary wave solutions to a class of nonlinear evolution equations (NEEs). A generalization of the method was applied to obtain more exact solutions of nonlinear differential equations based upon coupled Riccati equations [see \textit{Z. Yan}, Chaos Solitons Fractals 16, No. 5, 759--766 (2003; Zbl 1035.78006)]. This method was later extended by the authors [Chaos Solitons Fractals 22, No. 1, 243--247 (2004; Zbl 1067.35085)] to the Boiti-Leon-Pempinelli equation and many exact travelling wave solutions were obtained. Based on that extended method, they develop in the paper under review a variable-coefficient projective Riccati equation method for certain NEEs, finding several types of exact soliton-like solutions for a new \((2+1)\)-dimensional simplified generalized Broer-Kaup system with Painlevé property [see \textit{Sh. Zhang}, \textit{B. Wu} and \textit{S. Lou}, Phys. Lett., A 300, No. 1, 40--48 (2002; Zbl 0997.76012)].
scientific article; zbMATH DE number 2158518
scientific article