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

作　　者：吕大昭 崔艳英[2] 

机构地区：[1]北京建筑大学理学院,北京 [2]北京工业大学耿丹学院信息工程学院,北京

出　　处：《应用数学进展》2025年第1期194-202,共9页Advances in Applied Mathematics

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→0或1时,这些解退化为相应的孤立波解或三角函数解。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→0 or 1, these solutions degenerate to the corresponding solitary wave solutions and trigonometric function (singly periodic) solutions.

关 键 词：JACOBI椭圆函数 双周期解 非线性演化方程 

分 类 号：O17[理学—数学]