In this paper,new infinite sequence complex solutions of the coupled Kd V equations are constructed with the help of function transformation and the second kind of elliptic equation.First of all,according to the funct...In this paper,new infinite sequence complex solutions of the coupled Kd V equations are constructed with the help of function transformation and the second kind of elliptic equation.First of all,according to the function transformation,the coupled Kd V equations are changed into the second kind of elliptic equation.Secondly,the new solutions and Bäcklund transformation of the second kind of elliptic equation are applied to search for new infinite sequence complex solutions of the coupled Kd V equations.These solutions include new infinite sequence complex solutions composed by Jacobi elliptic function,hyperbolic function and triangular function.展开更多
In this paper, Lie symmetry is investigated for a new integrable coupled Korteweg-de Vries （KdV） equation system. Using some symmetry subalgebra of the equation system, we obtain five types of the significant simila...In this paper, Lie symmetry is investigated for a new integrable coupled Korteweg-de Vries （KdV） equation system. Using some symmetry subalgebra of the equation system, we obtain five types of the significant similarity reductions. Abundant solutions of the coupled KdV equation system, such as the solitary wave solution, exponential solution, rational solution and polynomial solution, etc. are obtained from the reduced equations. Especially, one type of group-invarlant solution of reduced equations can be acquired by means of the Painlevé I transcendent function.展开更多
In this article, we construct the exact traveling wave solutions for nonlinear evolution equations in the mathematical physics via the modified Kawahara equation, the nonlinear coupled KdV equations and the classical ...In this article, we construct the exact traveling wave solutions for nonlinear evolution equations in the mathematical physics via the modified Kawahara equation, the nonlinear coupled KdV equations and the classical Boussinesq equations, by using a generalized （G＇/G）-expansion method, where G satisfies the Jacobi elliptic equation. Many exact solutions in terms of Jacobi elliptic functions are obtained.展开更多
基金Supported by the Natural Natural Science Foundation of China(Grant No:11361040)Science Research Foundation of Institution of Higher Education of Inner Mongolia Autonomous Region,China(Grant No:NJZY16180)Natural Science Foundation of Inner Mongolia Autonomous Region,China(Grant No:2015MS0128)。
文摘In this paper,new infinite sequence complex solutions of the coupled Kd V equations are constructed with the help of function transformation and the second kind of elliptic equation.First of all,according to the function transformation,the coupled Kd V equations are changed into the second kind of elliptic equation.Secondly,the new solutions and Bäcklund transformation of the second kind of elliptic equation are applied to search for new infinite sequence complex solutions of the coupled Kd V equations.These solutions include new infinite sequence complex solutions composed by Jacobi elliptic function,hyperbolic function and triangular function.
基金Project supported by the National Natural Science Foundation of China （Grant No 10071033）, the Natural Science Foundation of Jiangsu Province, China （Grant No BK2002003）, and the Technology Innovation Plan for Postgraduate of Jiangsu Province in 2006 （Grant No 72）.Acknowledgment 0ne of the authors （Qian S P） is indebted to Professor Lou S Y for his helpful discussion.
文摘In this paper, Lie symmetry is investigated for a new integrable coupled Korteweg-de Vries （KdV） equation system. Using some symmetry subalgebra of the equation system, we obtain five types of the significant similarity reductions. Abundant solutions of the coupled KdV equation system, such as the solitary wave solution, exponential solution, rational solution and polynomial solution, etc. are obtained from the reduced equations. Especially, one type of group-invarlant solution of reduced equations can be acquired by means of the Painlevé I transcendent function.
文摘In this article, we construct the exact traveling wave solutions for nonlinear evolution equations in the mathematical physics via the modified Kawahara equation, the nonlinear coupled KdV equations and the classical Boussinesq equations, by using a generalized （G＇/G）-expansion method, where G satisfies the Jacobi elliptic equation. Many exact solutions in terms of Jacobi elliptic functions are obtained.
