Searching for exact solutions to nonlinear evolution equations is a very important and interesting work in non- linear science. In this paper, the modified Boussinesq equation is derived from the modified Gel＇fand-Di...Searching for exact solutions to nonlinear evolution equations is a very important and interesting work in non- linear science. In this paper, the modified Boussinesq equation is derived from the modified Gel＇fand-Dikii （raG-D） system. Furthermore, we study the modified Boussinesq equation by using the bilinear method and Wronskian technique, we obtain the N-soliton solutions to the above equation.展开更多
Two non-isospectral KdV equations with self-consistent sources are derived. Gauge transformation between the first non-isospectral KdV equation with self-consistent sources （corresponding to λt = -2aA） and its isos...Two non-isospectral KdV equations with self-consistent sources are derived. Gauge transformation between the first non-isospectral KdV equation with self-consistent sources （corresponding to λt = -2aA） and its isospectral counterpart is given, from which exact solutions for the first non-isospectral KdV equation with self-consistent sources is easily listed. Besides, the soliton solutions for the two equations are obtained by means of Hirota＇s method and Wronskian technique, respectively. Meanwhile, the dynamical properties for these solutions are investigated.展开更多
基金Project supported by the Science Foundation of Shanghai Municipal Education Commission (Grant No.06AZ081)
文摘Searching for exact solutions to nonlinear evolution equations is a very important and interesting work in non- linear science. In this paper, the modified Boussinesq equation is derived from the modified Gel＇fand-Dikii （raG-D） system. Furthermore, we study the modified Boussinesq equation by using the bilinear method and Wronskian technique, we obtain the N-soliton solutions to the above equation.
基金supported by the National Natural Science Foundation of China under Grant Nos. 10371070 and 10671121the Foundation for Excellent Postgraduates of Shanghai University under Grant No. Shucx080127
文摘Two non-isospectral KdV equations with self-consistent sources are derived. Gauge transformation between the first non-isospectral KdV equation with self-consistent sources （corresponding to λt = -2aA） and its isospectral counterpart is given, from which exact solutions for the first non-isospectral KdV equation with self-consistent sources is easily listed. Besides, the soliton solutions for the two equations are obtained by means of Hirota＇s method and Wronskian technique, respectively. Meanwhile, the dynamical properties for these solutions are investigated.
