In the present paper, a general solution involv- ing three arbitrary functions for the generalized （2＋1）- dimensional KdV-mKdV equation, which is derived from the generalized （1＋1）-dimensional KdV-mKdV equa- tio...In the present paper, a general solution involv- ing three arbitrary functions for the generalized （2＋1）- dimensional KdV-mKdV equation, which is derived from the generalized （1＋1）-dimensional KdV-mKdV equa- tion, is first introduced by means of the Wiess, Tabor, Carnevale （WTC） truncation method. And then multi- symplectic formulations with several conservation laws taken into account are presented for the generalized （2＋1）- dimensional KdV-mKdV equation based on the multi- symplectic theory of Bridges. Subsequently, in order to simulate the periodic wave solutions in terms of rational functions of the Jacobi elliptic functions derived from thegeneral solution, a semi-implicit multi-symplectic scheme is constructed that is equivalent 1：o the Preissmann scheme. From the results of the numerical experiments, we can con- clude that the multi-symplectic schemes can accurately sim- ulate the periodic wave solutions of the generalized （2＋1）- dimensional KdV-mKdV equation while preserve approxi- mately the conservation laws.展开更多
In this article, we consider analytical solutions of the time fractional derivative Gardner equation by using the new version of F-expansion method. With this proposed method multiple Jacobi elliptic functions are sit...In this article, we consider analytical solutions of the time fractional derivative Gardner equation by using the new version of F-expansion method. With this proposed method multiple Jacobi elliptic functions are situated in the solution function. As a result, various exact analytical solutions consisting of single and combined Jacobi elliptic functions solutions are obtained.展开更多
The(1+2)-dimensional chiral nonlinear Schr?dinger equation(2D-CNLSE)as a nonlinear evolution equation is considered and studied in a detailed manner.To this end,a complex transform is firstly adopted to arrive at the ...The(1+2)-dimensional chiral nonlinear Schr?dinger equation(2D-CNLSE)as a nonlinear evolution equation is considered and studied in a detailed manner.To this end,a complex transform is firstly adopted to arrive at the real and imaginary parts of the model,and then,the modified Jacobi elliptic expansion method is formally utilized to derive soliton and other solutions of the 2D-CNLSE.The exact solutions presented in this paper can be classified as topological and nontopological solitons as well as Jacobi elliptic function solutions.展开更多
基金supported by the National Natural Science Foundation of China (11002115,10972182,11172239)the Science Foundation of Aviation of China (2010ZB53021)+5 种基金the China Postdoctoral Science Special Foundation (201003682)111 project(B07050) to the Northwestern Polytechnical Universitythe NPU Foundation for Fundamental Research (JC200938,JC20110259)the Doctoral Program Foundation of Education Ministry of China(20106102110019)the Open Foundation of State Key Laboratory of Mechanical System & Vibration (MSV-2011-21)the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment (GZ0802)
文摘In the present paper, a general solution involv- ing three arbitrary functions for the generalized （2＋1）- dimensional KdV-mKdV equation, which is derived from the generalized （1＋1）-dimensional KdV-mKdV equa- tion, is first introduced by means of the Wiess, Tabor, Carnevale （WTC） truncation method. And then multi- symplectic formulations with several conservation laws taken into account are presented for the generalized （2＋1）- dimensional KdV-mKdV equation based on the multi- symplectic theory of Bridges. Subsequently, in order to simulate the periodic wave solutions in terms of rational functions of the Jacobi elliptic functions derived from thegeneral solution, a semi-implicit multi-symplectic scheme is constructed that is equivalent 1：o the Preissmann scheme. From the results of the numerical experiments, we can con- clude that the multi-symplectic schemes can accurately sim- ulate the periodic wave solutions of the generalized （2＋1）- dimensional KdV-mKdV equation while preserve approxi- mately the conservation laws.
文摘In this article, we consider analytical solutions of the time fractional derivative Gardner equation by using the new version of F-expansion method. With this proposed method multiple Jacobi elliptic functions are situated in the solution function. As a result, various exact analytical solutions consisting of single and combined Jacobi elliptic functions solutions are obtained.
文摘The(1+2)-dimensional chiral nonlinear Schr?dinger equation(2D-CNLSE)as a nonlinear evolution equation is considered and studied in a detailed manner.To this end,a complex transform is firstly adopted to arrive at the real and imaginary parts of the model,and then,the modified Jacobi elliptic expansion method is formally utilized to derive soliton and other solutions of the 2D-CNLSE.The exact solutions presented in this paper can be classified as topological and nontopological solitons as well as Jacobi elliptic function solutions.
