非线性耦合KdV方程组的一种新求解法  

A NEW KIND OF METHOD TO SOLVING SOLUTIONS OF THE NONLINEAR COUPLING KDV EQUATIONS

作　　者：伊丽娜[1] 套格图桑[1] YI Li-na;Taogetusang(College of Mathematical Science, Inner Mongolia Normal University, Huhhot 010022, China)

机构地区：[1]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022

出　　处：《数学杂志》2017年第4期823-832,共10页Journal of Mathematics

基　　金：国家自然科学基金资助(11361040);内蒙古自治区高等学校科学研究基金资助(NJZY16180);内蒙古自治区自然科学基金资助(2015MS0128);内蒙古自治区2016年硕士研究生科研创新项目(S20161013502);内蒙古师范大学硕士研究生科研创新基金项目(CXJJS16081)

摘　　要：本文研究了构造非线性耦合Kd V方程组的无穷序列复合型新解的问题.利用函数变换与辅助方程相结合的方法,获得了非线性耦合Kd V方程组的自由Riemannθ函数、Jacobi椭圆函数、双曲函数和三角函数两两组合的无穷序列复合型新解.这些解包括了双弧子解、双周期解和弧子解与周期解复合的解.In this paper,the problem of constructing the new infinite sequence complexion solution of the nonlinear coupled KdV equations is researched.With the help of the method combining the function transformation with the auxiliary equation,the new infinite sequence complexion solutions consisting by two of the Riemannμfunction,Jacobi elliptic function,hyperbolic functions and trigonometric functions of the nonlinear coupled KdV equations are obtained.These solutions conclude two-solitions,double-periodic solutions and soliton solution and periodic solution complexion solutions.

关 键 词：非线性耦合KdV方程组 函数变换 非线性叠加公式 无穷序列复合型新解 

分 类 号：O175.2[理学—数学]