As an improved version of trial equation method, a new trial equation method is proposed. Using this method, abundant new exact traveling wave solutions to a high-order KdV-type equation are obtained.
In this paper, we present a solution methodology to obtain exact solutions of some nonlinear evolution equation by modifying the homogeneous balance method. Based on the modified homogeneous balance method, several ki...In this paper, we present a solution methodology to obtain exact solutions of some nonlinear evolution equation by modifying the homogeneous balance method. Based on the modified homogeneous balance method, several kinds of exact（new） solutions of the generalized KdV equation are obtained.展开更多
By constructing appropriate transformations and an extended elliptic sub-equation approach, we find some exact solutions of variable coefficient cubic-quintie nonlinear Schrodinger equation with an external potential,...By constructing appropriate transformations and an extended elliptic sub-equation approach, we find some exact solutions of variable coefficient cubic-quintie nonlinear Schrodinger equation with an external potential, which include bell and kink profile solitary wave solutions, singular solutions, triangular periodic wave solutions and so on.展开更多
The bounded and smooth solitary wave solutions of 10 nonlinear evolution equations with a positive fractional power term of dependent variable are successfully obtained by homogeneous balance principle and with the ai...The bounded and smooth solitary wave solutions of 10 nonlinear evolution equations with a positive fractional power term of dependent variable are successfully obtained by homogeneous balance principle and with the aid of sub-ODEs that admits a solution of sech-power or tanh-power type.In the special cases that the fractional power equals to 1 and 2,the solitary wave solutions of more than 10 important model equations arisen from mathematical physics are easily rediscovered.展开更多
文摘As an improved version of trial equation method, a new trial equation method is proposed. Using this method, abundant new exact traveling wave solutions to a high-order KdV-type equation are obtained.
基金Foundation item： Supported by the National Natural Science Foundation of China（10671182） Supported by the Foundation and Frontier Technology Research of Henan（082300410060）
文摘In this paper, we present a solution methodology to obtain exact solutions of some nonlinear evolution equation by modifying the homogeneous balance method. Based on the modified homogeneous balance method, several kinds of exact（new） solutions of the generalized KdV equation are obtained.
基金supported by National Natural Science Foundation of China under Grant No.10172056
文摘By constructing appropriate transformations and an extended elliptic sub-equation approach, we find some exact solutions of variable coefficient cubic-quintie nonlinear Schrodinger equation with an external potential, which include bell and kink profile solitary wave solutions, singular solutions, triangular periodic wave solutions and so on.
基金Supported by the Natural Science Foundation of Education Department of Henan Province of China under Grant No.2011B110013
文摘The bounded and smooth solitary wave solutions of 10 nonlinear evolution equations with a positive fractional power term of dependent variable are successfully obtained by homogeneous balance principle and with the aid of sub-ODEs that admits a solution of sech-power or tanh-power type.In the special cases that the fractional power equals to 1 and 2,the solitary wave solutions of more than 10 important model equations arisen from mathematical physics are easily rediscovered.
