In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic co...In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic computation code Maple.展开更多
In this paper, we apply homotopy analysis method to solve discrete mKdV equation and successfully obtain the bell-shaped solitary solution to mKdV equation. Comparison between our solution and the exact solution shows...In this paper, we apply homotopy analysis method to solve discrete mKdV equation and successfully obtain the bell-shaped solitary solution to mKdV equation. Comparison between our solution and the exact solution shows that homotopy analysis method is effective and validity in solving hybrid nonlinear problems, including solitary solution of difference-differential equation.展开更多
An exact two-soliton solution of discrete mKdv equation is derived by using the Hirota direct approach. In addition, we plot the soliton solutions to discuss the properties of solitons. It is worth while noting that w...An exact two-soliton solution of discrete mKdv equation is derived by using the Hirota direct approach. In addition, we plot the soliton solutions to discuss the properties of solitons. It is worth while noting that we obtain the completely elastic interaction between the two solitons.展开更多
In this paper, aiming to get more insight on the relation between the higher order semidiscrete mKdV equations and higher order mKdV equations, we construct a fifth order semidiscrete mKdV equation from the three know...In this paper, aiming to get more insight on the relation between the higher order semidiscrete mKdV equations and higher order mKdV equations, we construct a fifth order semidiscrete mKdV equation from the three known semidiscrete mKdV fluxes. We not only give its Lax pairs, Darboux transformation, explicit solutions and infinitely many conservation laws, but also show that their continuous limits yield the corresponding results for the fifth order mKdV equation. We thus conclude that the fifth order discrete mKdV equation is extremely an useful discrete scheme for the fifth order mtCdV equation.展开更多
In this paper, by means of the potential systems of the given nonlinear evolution equations, a procedure of symmetry preserving discretization of differential equations is presented. The specific process will be given...In this paper, by means of the potential systems of the given nonlinear evolution equations, a procedure of symmetry preserving discretization of differential equations is presented. The specific process will be given detailed in section 2. This extended method is effective for discreting the high-order (high-dimensional) nonlinear evolution equations. As examples, the invariant difference models of the mKdV equation and the Boussinesq equation are constructed.展开更多
基金Project supported by the Natural Science Foundation of China(10461006)the Natural Science Foundation of Inner Mongolia(2004080201103)the High Education Science Research Programof Inner Mongolia(NJ02035)
基金the National Key Basic Research Project of China under
文摘In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic computation code Maple.
基金the State Key Basic Research Program of China under Grant No.2004CB318000
文摘In this paper, we apply homotopy analysis method to solve discrete mKdV equation and successfully obtain the bell-shaped solitary solution to mKdV equation. Comparison between our solution and the exact solution shows that homotopy analysis method is effective and validity in solving hybrid nonlinear problems, including solitary solution of difference-differential equation.
文摘An exact two-soliton solution of discrete mKdv equation is derived by using the Hirota direct approach. In addition, we plot the soliton solutions to discuss the properties of solitons. It is worth while noting that we obtain the completely elastic interaction between the two solitons.
基金Project Supported by National Nature Science Foundation of China(10461006)the High Education Science ResearchProgramof Inner Mongolia(NJ02035)the Natural Science Foundation of Inner Mongolia(2004080201103)
基金supported by National Natural Science Foundation of China (Grant No.10971136)the Ministry of Education and Innovation of Spain (Grant No.MTM2009-12670)
文摘In this paper, aiming to get more insight on the relation between the higher order semidiscrete mKdV equations and higher order mKdV equations, we construct a fifth order semidiscrete mKdV equation from the three known semidiscrete mKdV fluxes. We not only give its Lax pairs, Darboux transformation, explicit solutions and infinitely many conservation laws, but also show that their continuous limits yield the corresponding results for the fifth order mKdV equation. We thus conclude that the fifth order discrete mKdV equation is extremely an useful discrete scheme for the fifth order mtCdV equation.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11075055, 11275072Innovative Research Team Program of the National Natural Science Foundation of China under Grant No.61021004+2 种基金National High Technology Research and Development Program under Grant No.2011AA010101Shanghai Leading Academic Discipline Project No.B412Shanghai Knowledge Service Platform for Trustworthy Internet of Things under Grant No.ZF12131
文摘In this paper, by means of the potential systems of the given nonlinear evolution equations, a procedure of symmetry preserving discretization of differential equations is presented. The specific process will be given detailed in section 2. This extended method is effective for discreting the high-order (high-dimensional) nonlinear evolution equations. As examples, the invariant difference models of the mKdV equation and the Boussinesq equation are constructed.
