Jacobi椭圆函数有理展开法和应用
A Jacobi Elliptic Function Rational Expansion Method and Its Applications
DOI: 10.12677/pm.2024.1412409, PDF,   
作者: 吕大昭：北京建筑大学理学院，北京；崔艳英：北京工业大学耿丹学院信息工程学院，北京
关键词: Jacobi椭圆函数；有理解；双周期解；非线性波动方程；Jacobi Elliptic Function； Rational Solutions； Doubly Periodic Solutions； Nonlinear Wave Equation
摘要: 一个新的广义的Jacobi椭圆函数有理展开法被提出来构造非线性波动方程的有理解。利用这个直接有效的方法，获得了许多关于Jacobi椭圆函数的有理解。当模数m→0或1时，这些解退化为相应的关于孤立波或三角函数的有理解。
Abstract: A new general Jacobi elliptic function rational expansion procedure is presented for constructing rational solutions of nonlinear wave equations in terms of the Jacobi elliptic function. As a consequence, many new rational form Jacobi elliptic function solutions are obtained by this powerful and direct method. Moreover, the corresponding rational form solitary wave solutions and rational form trigonometric function solutions are also obtained when the modulus m→0 or 1.
文章引用：吕大昭, 崔艳英. Jacobi椭圆函数有理展开法和应用[J]. 理论数学, 2024, 14(12): 84-89. https://doi.org/10.12677/pm.2024.1412409

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