中文摘要：

将Jacobi椭圆函数展开法进一步扩展,并利用这一方法求出组合KdV方程和mKdV方程的一系列新的显式精确解,在模数m→1或0的极限情况下,可得到相应的孤立波解和单周期波解.研究表明,该方法在寻求数学物理领域的非线性偏微分方程的精确解方面是有效的.

英文摘要：

In this paper,based on the generalized Jacobi elliptic functions expansion method,we obtain abundant exact explicit solutions of the combined KdV（cKdV） and modified KdV（mKdV） equation,these solutions are degenerated to the solitary wave solutions and the triangle function solutions in the limit cases when the modulus of the Jacobian elliptic functions m→1 or 0,which shows that the new method is more powerful to seek the exact solutions of the nonlinear partial differential equations in mathematical physics.