In this paper,the variable cofficient KdV equation with dissipative loss and nonuniformity terms and the variable coefficient SG equation with nonuniformity term are studied. The exact solutions of the KdV and SG equa...In this paper,the variable cofficient KdV equation with dissipative loss and nonuniformity terms and the variable coefficient SG equation with nonuniformity term are studied. The exact solutions of the KdV and SG equations are obtained.In particular,the soliton solutions of two equations are found. Received November 25,1996.Revised June 30,1997.1991 MR Subject Classification:35Q53.展开更多
A （2＋1）-dimensional KdV equation is obtained by use of Hirota method, which possesses N-soliton solution, specially its exact two-soliton solution is presented. By employing a proper algebraic transformation and th...A （2＋1）-dimensional KdV equation is obtained by use of Hirota method, which possesses N-soliton solution, specially its exact two-soliton solution is presented. By employing a proper algebraic transformation and the Riccati equation, a type of hell-shape soliton solutions are produced via regarding the variable in the Riccati equation as the independent variable. Finally, we extend the above （2＋1）-dimensional KdV equation into （3＋1）-dimensional equation, the two-soliton solutions are given.展开更多
In this work, we study the generalized Rosenau-KdV equation. We shall use the sech-ansatze method to derive the solitary wave solutions of this equation.
文摘In this paper,the variable cofficient KdV equation with dissipative loss and nonuniformity terms and the variable coefficient SG equation with nonuniformity term are studied. The exact solutions of the KdV and SG equations are obtained.In particular,the soliton solutions of two equations are found. Received November 25,1996.Revised June 30,1997.1991 MR Subject Classification:35Q53.
基金Supported in part by the Natural Science Foundation of Henan Province of China(0111050200) the Natural Science Foundation of Education Department of Henan Province of China(2003110003) the Science Foundation of Henan University of Science and Technology(2003QN13)
基金＊The project supported by National Natural Science Foundation of China under Grant No. 10471139 and Hong Kong Research Grant Council under Grant No. HKBU/2016/03P
文摘A （2＋1）-dimensional KdV equation is obtained by use of Hirota method, which possesses N-soliton solution, specially its exact two-soliton solution is presented. By employing a proper algebraic transformation and the Riccati equation, a type of hell-shape soliton solutions are produced via regarding the variable in the Riccati equation as the independent variable. Finally, we extend the above （2＋1）-dimensional KdV equation into （3＋1）-dimensional equation, the two-soliton solutions are given.
文摘In this work, we study the generalized Rosenau-KdV equation. We shall use the sech-ansatze method to derive the solitary wave solutions of this equation.
