In this paper, a new auxiliary equation method is presented of constructing more new non-travelling wave solutions of nonlinear differential equations in mathematical physics, which is direct and more powerful than pr...In this paper, a new auxiliary equation method is presented of constructing more new non-travelling wave solutions of nonlinear differential equations in mathematical physics, which is direct and more powerful than projective Riccati equation method. In order to illustrate the validity and the advantages of the method, （2＋1）-dimensional asymmetric Nizhnik-Novikov-Vesselov equation is employed and many new double periodic non-travelling wave solutions are obtained. This algorithm can also be applied to other nonlinear differential equations.展开更多
The improved tanh function method [Commun. Theor. Phys. （Beijing, China） 43 （2005） 585] is further improved by generalizing the ansatz solution of the considered equation. As its application, the （2＋1）-dimensio...The improved tanh function method [Commun. Theor. Phys. （Beijing, China） 43 （2005） 585] is further improved by generalizing the ansatz solution of the considered equation. As its application, the （2＋1）-dimensional Broer-Kaup equations are considered and abundant new exact non-travelling wave solutions are obtained.展开更多
In this paper,the idea of a combination of variable separation approach and the extended homoclinic test approach is proposed to seek non-travelling wave solutions of Calogero equation.The equation is reduced to some(...In this paper,the idea of a combination of variable separation approach and the extended homoclinic test approach is proposed to seek non-travelling wave solutions of Calogero equation.The equation is reduced to some(1+1)-dimensional nonlinear equations by applying the variable separation approach and solves reduced equations with the extended homoclinic test technique.Based on this idea and with the aid of symbolic computation,some new explicit solutions can be obtained.展开更多
By applying the extended homogeneous balance method, we find some new explicit solutions to two nonlinear evolution equations, which include n-resonance plane solitary wave and non-traveling wave solutions.
Starting from the symbolic computation system Maple and Riccati equation mapping approach and a linear variable separation approach, a new family of non-traveling wave solutions of the (1 + 1)-dimensional Burgers syst...Starting from the symbolic computation system Maple and Riccati equation mapping approach and a linear variable separation approach, a new family of non-traveling wave solutions of the (1 + 1)-dimensional Burgers system is derived.展开更多
In this work, starting from the (G'/G)-expansion method and a variable separation method, a new non-traveling wave general solutions of the (2+1)-dimensional breaking soliton system are derived. By selecting appro...In this work, starting from the (G'/G)-expansion method and a variable separation method, a new non-traveling wave general solutions of the (2+1)-dimensional breaking soliton system are derived. By selecting appropriately the arbitrary functions in the solutions, special soliton-structure excitations and evolutions are studied.展开更多
The extended tanh method is further improved by generalizing the Riccati equation and introducing its twenty seven new solutions. As its application, the (2+ 1)-dimensional Broer-Kaup equation is investigated and then...The extended tanh method is further improved by generalizing the Riccati equation and introducing its twenty seven new solutions. As its application, the (2+ 1)-dimensional Broer-Kaup equation is investigated and then its fifty four non-travelling wave solutions have been obtained. The results reported in this paper show that this method is more powerful than those, such as tanh method, extended tanh method, modified extended tanh method and Riccati equation expansion method introduced in previous literatures.展开更多
基金Project supported by the State Key Program for Basic Research of China (Grant No 2004CB318000)
文摘In this paper, a new auxiliary equation method is presented of constructing more new non-travelling wave solutions of nonlinear differential equations in mathematical physics, which is direct and more powerful than projective Riccati equation method. In order to illustrate the validity and the advantages of the method, （2＋1）-dimensional asymmetric Nizhnik-Novikov-Vesselov equation is employed and many new double periodic non-travelling wave solutions are obtained. This algorithm can also be applied to other nonlinear differential equations.
文摘The improved tanh function method [Commun. Theor. Phys. （Beijing, China） 43 （2005） 585] is further improved by generalizing the ansatz solution of the considered equation. As its application, the （2＋1）-dimensional Broer-Kaup equations are considered and abundant new exact non-travelling wave solutions are obtained.
文摘In this paper,the idea of a combination of variable separation approach and the extended homoclinic test approach is proposed to seek non-travelling wave solutions of Calogero equation.The equation is reduced to some(1+1)-dimensional nonlinear equations by applying the variable separation approach and solves reduced equations with the extended homoclinic test technique.Based on this idea and with the aid of symbolic computation,some new explicit solutions can be obtained.
文摘By applying the extended homogeneous balance method, we find some new explicit solutions to two nonlinear evolution equations, which include n-resonance plane solitary wave and non-traveling wave solutions.
文摘Starting from the symbolic computation system Maple and Riccati equation mapping approach and a linear variable separation approach, a new family of non-traveling wave solutions of the (1 + 1)-dimensional Burgers system is derived.
文摘In this work, starting from the (G'/G)-expansion method and a variable separation method, a new non-traveling wave general solutions of the (2+1)-dimensional breaking soliton system are derived. By selecting appropriately the arbitrary functions in the solutions, special soliton-structure excitations and evolutions are studied.
文摘The extended tanh method is further improved by generalizing the Riccati equation and introducing its twenty seven new solutions. As its application, the (2+ 1)-dimensional Broer-Kaup equation is investigated and then its fifty four non-travelling wave solutions have been obtained. The results reported in this paper show that this method is more powerful than those, such as tanh method, extended tanh method, modified extended tanh method and Riccati equation expansion method introduced in previous literatures.
