修正的短脉冲方程的精确周期行波解  

Exact Periodic Travelling-wave Solutions of the Modified Short Pulse Equation

作　　者：薛敏 XUE MIN(Department of Mathematics,China University of Mining and Technology,Beijing 100083,China)

机构地区：[1]中国矿业大学(北京)理学院,北京100083

出　　处：《应用数学学报》2024年第5期789-798,共10页Acta Mathematicae Applicatae Sinica

基　　金：中央高校基本科研资助项目。

摘　　要：本文系统讨论了修正的短脉冲(mSP)方程的周期行波解.首先通过引入新的变量,将mSP方程的周期行波解问题转化为了一个一阶常微分方程的求解,然后借助于经典的椭圆函数和椭圆积分,构造了mSP方程不同种类的周期行波解.基于得到的周期解,并对其取极限,得到了mSP方程的1-cuspon解与新的一种解.In this paper,the exact periodic traveling wave solutions of modified short pulse(mSP)equation are systematically discussed.With the aid of new variables,the msP equation is converted to an ordinary differential equation of first order.By means of elliptic integrals and Jacobi elliptic functions,this equation is solved and the periodic traveling solutions of the mSP equation are constructed.Through exploring the limits of these periodic solutions,the 1-cuspon solution and a new solution are obtained.

关 键 词：mSP方程 周期解 cuspon解 

分 类 号：O175.24[理学—数学]