%0 Journal Article
%T 非线性演化方程的丰富的Jacobi椭圆函数解<br>Abundant Jacobi Elliptic Function Solutions of Nonlinear Evolution Equations
%A 吕大昭
%A 崔艳英
%J Advances in Applied Mathematics
%P 194-202
%@ 2324-8009
%D 2025
%I Hans Publishing
%R 10.12677/aam.2025.141022
%X 本文通过把十二个Jacobi椭圆函数分类成四组&#65292;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<i>Maple</i>的帮助下<i>&#65292;</i>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&#65292;当模数m<math xmlns='http://www.w3.org/1998/Math/MathML'>
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0或1时&#65292;这些解退化为相应的孤立波解或三角函数解。<br>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, <i>Maple</i>), many exact doubly periodic solutions are obtained which shows that this method is very powerful. When the modulus m<math xmlns='http://www.w3.org/1998/Math/MathML'>
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0 or 1, these solutions degenerate to the corresponding solitary wave solutions and trigonometric function (singly periodic) solutions.
%K Jacobi椭圆函数&#65292
%K 双周期解&#65292
%K 非线性演化方程<br>Jacobi Elliptic Function
%K Doubly Periodic Solution
%K Nonlinear Evolution Equation
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=106414