The 'trial function method' ( TFM for short) and a routine way in finding traveling,wave solutions to some nonlinear partial differential equations( PDE for short), wer explained. Two types of evolution equati...The 'trial function method' ( TFM for short) and a routine way in finding traveling,wave solutions to some nonlinear partial differential equations( PDE for short), wer explained. Two types of evolution equations are studied, one is a generalized Burgers or KdV equation, the other is the Fisher equation with special nonlinear forms of its reaction rate term. One can see that this method is simple, fast and allowing further extension.展开更多
In this paper,we obtained the topological soliton solution of the(1+1)-dimensional generalized modified Benjamin-Bona-Mahony equation and shock wave solution of the generalized Boussinesq equation.We get that solution...In this paper,we obtained the topological soliton solution of the(1+1)-dimensional generalized modified Benjamin-Bona-Mahony equation and shock wave solution of the generalized Boussinesq equation.We get that solutions by using solitary wave ansatz in terms of tanh^(p) functions.The velocity and the free parameters are the physical parameters in the soliton solutions.They can be obtained as functions of the dependent model coefficients.The domain restriction were also identified in the process.we hope that in nonlinear dynamical system these solutions will be explain some nonlinear physical phenomena.展开更多
This paper is concerned with the (2+1)-dimensional Benney types of equations. By the complete Lie group classification method, all of the point symmetries of the Benney types of equations are obtained, and the integra...This paper is concerned with the (2+1)-dimensional Benney types of equations. By the complete Lie group classification method, all of the point symmetries of the Benney types of equations are obtained, and the integrable condition of the equation is given. Then, the symmetry reductions and exact solutions to the (2+1)-dimensional nonlinear wave equations are presented. Especially, the shock wave solutions of the Benney equations are investigated by the symmetry reduction and trial function method.展开更多
Shock relations usually found in literatures are derived theoretically under the assumption of homogeneous thermodynamic properties, i.e., constant ratio of specific heats, γ. However, high temperature effects post a...Shock relations usually found in literatures are derived theoretically under the assumption of homogeneous thermodynamic properties, i.e., constant ratio of specific heats, γ. However, high temperature effects post a strong shock wave may result in thermodynamic heterogeneities and failure to the original shock relations. In this paper, the shock relations are extended to take account of high-temperature effects. Comparison indicates that the present approach is more feasible than other analytical approaches to reflect the influence of γ heterogeneity on the post-shock parameters.展开更多
The main idea of this method is to take full advantage of the elliptic equation that Jacobi elliptic functions satisfy and use its solutions to replace Jacobi elliptic functions in Jacobi elliptic function method. Som...The main idea of this method is to take full advantage of the elliptic equation that Jacobi elliptic functions satisfy and use its solutions to replace Jacobi elliptic functions in Jacobi elliptic function method. Some illustrative equations are investigated by this means.展开更多
文摘The 'trial function method' ( TFM for short) and a routine way in finding traveling,wave solutions to some nonlinear partial differential equations( PDE for short), wer explained. Two types of evolution equations are studied, one is a generalized Burgers or KdV equation, the other is the Fisher equation with special nonlinear forms of its reaction rate term. One can see that this method is simple, fast and allowing further extension.
文摘In this paper,we obtained the topological soliton solution of the(1+1)-dimensional generalized modified Benjamin-Bona-Mahony equation and shock wave solution of the generalized Boussinesq equation.We get that solutions by using solitary wave ansatz in terms of tanh^(p) functions.The velocity and the free parameters are the physical parameters in the soliton solutions.They can be obtained as functions of the dependent model coefficients.The domain restriction were also identified in the process.we hope that in nonlinear dynamical system these solutions will be explain some nonlinear physical phenomena.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11171041 and 11505090Research Award Foundation for Outstanding Young Scientists of Shandong Province under Grant No.BS2015SF009the doctorial foundation of Liaocheng University under Grant No.31805
文摘This paper is concerned with the (2+1)-dimensional Benney types of equations. By the complete Lie group classification method, all of the point symmetries of the Benney types of equations are obtained, and the integrable condition of the equation is given. Then, the symmetry reductions and exact solutions to the (2+1)-dimensional nonlinear wave equations are presented. Especially, the shock wave solutions of the Benney equations are investigated by the symmetry reduction and trial function method.
基金supported by the National Natural Science Foundation of China(Grant Nos.11672308 and 11532014)Innovation Grant of Chinese Academy of Sciences
文摘Shock relations usually found in literatures are derived theoretically under the assumption of homogeneous thermodynamic properties, i.e., constant ratio of specific heats, γ. However, high temperature effects post a strong shock wave may result in thermodynamic heterogeneities and failure to the original shock relations. In this paper, the shock relations are extended to take account of high-temperature effects. Comparison indicates that the present approach is more feasible than other analytical approaches to reflect the influence of γ heterogeneity on the post-shock parameters.
基金Supported by the National Key Basic Research Development Project of China(1998030600)the National Natural Science Foundation of China(10072013)
文摘The main idea of this method is to take full advantage of the elliptic equation that Jacobi elliptic functions satisfy and use its solutions to replace Jacobi elliptic functions in Jacobi elliptic function method. Some illustrative equations are investigated by this means.
