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

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.