A trial equation method to nonlinear evolution equation with rank inhomogeneous is given. As appncations, the exact traveling wave solutions to some higher-order nonlinear equations such as generalized Boussinesq equa...A trial equation method to nonlinear evolution equation with rank inhomogeneous is given. As appncations, the exact traveling wave solutions to some higher-order nonlinear equations such as generalized Boussinesq equation, generalized Pochhammer-Chree equation, KdV-Burgers equation, and KS equation and so on, are obtained. Among these, some results are new. The proposed method is based on the idea of reduction of the order of ODE. Some mathematical details of the proposed method are discussed.展开更多
Trial equation method is a powerful tool for obtaining exact solutions of nonlinear differential equations. In this paper, the improved Boussinesq is reduced to an ordinary differential equation under the travelling w...Trial equation method is a powerful tool for obtaining exact solutions of nonlinear differential equations. In this paper, the improved Boussinesq is reduced to an ordinary differential equation under the travelling wave transformation. Trial equation method and the theory of complete discrimination system for polynomial are used to establish exact solutions of the improved Boussinesq equation.展开更多
Using trial equation method, abundant exact envelope traveling wave solutions of high-order dispersive cubic-quintic nonlinear Schr6dinger equation, which include envelope soliton solutions, triangular function envelo...Using trial equation method, abundant exact envelope traveling wave solutions of high-order dispersive cubic-quintic nonlinear Schr6dinger equation, which include envelope soliton solutions, triangular function envelope solutions, and Jacobian elliptic function envelope solutions, are obtained. To our knowledge, all of these results are new. In particular, our proposed method is very simple and can be applied to a lot of similar equations.展开更多
In the article, the nonlinear equation is reduced to an ordinary differential equation under the travelling wave transformation. Using trial equation method, the ODE is reduced to the elementary integral form. In the ...In the article, the nonlinear equation is reduced to an ordinary differential equation under the travelling wave transformation. Using trial equation method, the ODE is reduced to the elementary integral form. In the end, complete discrimination system for polynomial is used to solve the corresponding integrals and obtain the classification of all single travelling wave solutions to the equation.展开更多
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.
The nonlinear two-point boundary value problem(TPBVP)is converted to a new form of the problem including integral terms.Then the combination of weak-form integral equation method(WFIEM)and special functions create a r...The nonlinear two-point boundary value problem(TPBVP)is converted to a new form of the problem including integral terms.Then the combination of weak-form integral equation method(WFIEM)and special functions create a robust and applicable numerical scheme to solve the problem.To display the accuracy of our method,some examples are investigated.Also,the fractional Boussinesq-like equation involving the β-derivative has been considered that describes the propagation of small amplitude long capillary-gravity waves on the surface of shallow water.展开更多
文摘A trial equation method to nonlinear evolution equation with rank inhomogeneous is given. As appncations, the exact traveling wave solutions to some higher-order nonlinear equations such as generalized Boussinesq equation, generalized Pochhammer-Chree equation, KdV-Burgers equation, and KS equation and so on, are obtained. Among these, some results are new. The proposed method is based on the idea of reduction of the order of ODE. Some mathematical details of the proposed method are discussed.
文摘Trial equation method is a powerful tool for obtaining exact solutions of nonlinear differential equations. In this paper, the improved Boussinesq is reduced to an ordinary differential equation under the travelling wave transformation. Trial equation method and the theory of complete discrimination system for polynomial are used to establish exact solutions of the improved Boussinesq equation.
文摘Using trial equation method, abundant exact envelope traveling wave solutions of high-order dispersive cubic-quintic nonlinear Schr6dinger equation, which include envelope soliton solutions, triangular function envelope solutions, and Jacobian elliptic function envelope solutions, are obtained. To our knowledge, all of these results are new. In particular, our proposed method is very simple and can be applied to a lot of similar equations.
文摘In the article, the nonlinear equation is reduced to an ordinary differential equation under the travelling wave transformation. Using trial equation method, the ODE is reduced to the elementary integral form. In the end, complete discrimination system for polynomial is used to solve the corresponding integrals and obtain the classification of all single travelling wave solutions to the equation.
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.
文摘The nonlinear two-point boundary value problem(TPBVP)is converted to a new form of the problem including integral terms.Then the combination of weak-form integral equation method(WFIEM)and special functions create a robust and applicable numerical scheme to solve the problem.To display the accuracy of our method,some examples are investigated.Also,the fractional Boussinesq-like equation involving the β-derivative has been considered that describes the propagation of small amplitude long capillary-gravity waves on the surface of shallow water.
