Making use of a new generalized ansatz, we present a new generalized extended F-expansion method for constructing the exact solutions of nonlinear partial differential equations in a unified way. Applying the generali...Making use of a new generalized ansatz, we present a new generalized extended F-expansion method for constructing the exact solutions of nonlinear partial differential equations in a unified way. Applying the generalized method with the aid of Maple, we consider the （2＋1）-dimentional breaking soliton equation. As a result, we successfully obtain some new and more general solutions including Jacobi elliptic function solutions, soliton-like solutions, trigonometric function solutions, and so on. As an illustrative sampler the properties of some soliton solutions for the breaking soliton equation are shown by some figures. Our method can also be applied to other partial differential equations.展开更多
Periodic wave solutions to the dispersive long-wave equations are obtained by using the F-expansion method, which can be thought of as a generalization of the Jacobi elliptic function method. In the limit case, solita...Periodic wave solutions to the dispersive long-wave equations are obtained by using the F-expansion method, which can be thought of as a generalization of the Jacobi elliptic function method. In the limit case, solitary wave solutions are obtained as well.展开更多
New exact solutions expressed by the Jacobi elliptic functions are obtained to the （2＋1）-dimensional dispersive long-wave equations by using the modified F-expansion method. In the limit case, new solitary wave sol...New exact solutions expressed by the Jacobi elliptic functions are obtained to the （2＋1）-dimensional dispersive long-wave equations by using the modified F-expansion method. In the limit case, new solitary wave solutions and triangular periodic wave solutions are obtained as well.展开更多
New exact solutions expressed by the Jacobi elliptic functions are obtained to the long-short wave interaction equations by using the modified F-expansion method. In the limit case, solitary wave solutions and triangu...New exact solutions expressed by the Jacobi elliptic functions are obtained to the long-short wave interaction equations by using the modified F-expansion method. In the limit case, solitary wave solutions and triangular periodic wave solutions are obtained as well.展开更多
基金The project supported partially by the State Key Basic Research Program of China under Grant No. 2004 CB 318000The authors would like to thank the referee for his/her valuable suggestions.
文摘Making use of a new generalized ansatz, we present a new generalized extended F-expansion method for constructing the exact solutions of nonlinear partial differential equations in a unified way. Applying the generalized method with the aid of Maple, we consider the （2＋1）-dimentional breaking soliton equation. As a result, we successfully obtain some new and more general solutions including Jacobi elliptic function solutions, soliton-like solutions, trigonometric function solutions, and so on. As an illustrative sampler the properties of some soliton solutions for the breaking soliton equation are shown by some figures. Our method can also be applied to other partial differential equations.
文摘Periodic wave solutions to the dispersive long-wave equations are obtained by using the F-expansion method, which can be thought of as a generalization of the Jacobi elliptic function method. In the limit case, solitary wave solutions are obtained as well.
基金The project supported by the Natural Science Foundation of Shandong Province of China under Grant No. 2004 zx16
文摘New exact solutions expressed by the Jacobi elliptic functions are obtained to the （2＋1）-dimensional dispersive long-wave equations by using the modified F-expansion method. In the limit case, new solitary wave solutions and triangular periodic wave solutions are obtained as well.
文摘New exact solutions expressed by the Jacobi elliptic functions are obtained to the long-short wave interaction equations by using the modified F-expansion method. In the limit case, solitary wave solutions and triangular periodic wave solutions are obtained as well.
