一类变系数自耦合KdV方程组的解析解  

Analytic Solutions for a New Kind of Auto-Coupled KdV Equation with Variable Coefficients

作　　者：胡东坡[1] 化存才[1] 

机构地区：[1]云南师范大学数学学院,昆明650500

出　　处：《重庆理工大学学报（自然科学）》2013年第7期119-124,共6页Journal of Chongqing University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(10772158;11162020);云南省中青年学术与技术带头人计划项目(2008PY059)

摘　　要：利用扩展的Jacobi椭圆函数展开法构造一类变系数耦合KdV方程组的精确解。通过求解非线性代数方程组获得了不同情形下的孤立波解,在极限的情况下可以得到相应的类孤立波解、类冲击波解或类三角函数型解。In this paper, we apply the extended Jacobi elliptic function expansion method to discuss a new kind of auto-coupled KdV equation with variable coefficients. By solving nonlinear differential algebraic equations which are derived from solving nonlinear evolution equation, some solitary wave solutions in different situations for the auto-coupled KdV equation with variable coefficients are derived. In the limit cases, solitude-like solutions, shock-wave-like solutions and trigonometric-function-like periodic solutions are derived.

关 键 词：扩展的Jacobi椭圆函数展开法 耦合KDV方程组 孤立波解 

分 类 号：O175.29[理学—数学]