非线性演化方程的丰富的Jacobi椭圆函数解

Abundant Jacobi Elliptic Function Solutions of Nonlinear Evolution Equations

摘要: 本文通过把十二个Jacobi椭圆函数分类成四组，从而提出一个新的广义Jacobi椭圆函数展开法来构造非线性演化方程的精确双周期解。在数学软件Maple的帮助下，应用这个非常有效的方法求出了非线性演化方程的许多解，当模数m$\to$ 0或1时，这些解退化为相应的孤立波解或三角函数解。

Abstract: In this letter, twelve Jacobi elliptic functions are divided into four groups, and a new general Jacobi elliptic function expansion method is proposed to construct abundant exact doubly periodic solutions of nonlinear evolution equations. As a result, with the aid of computer symbolic computation software (for example, Maple), many exact doubly periodic solutions are obtained which shows that this method is very powerful. When the modulus m$\to$ 0 or 1, these solutions degenerate to the corresponding solitary wave solutions and trigonometric function (singly periodic) solutions.