五阶KdV方程的行波解、周期波解及其渐近分析  

Traveling Wave Solution and Periodic Wave Solution as well as Asymptotic Analysis of Fifth-order KdV Equation

作　　者：秦春艳 QIN Chunyan(School of Mathematics and Statistics,Suzhou University,Suzhou 234000,China)

机构地区：[1]宿州学院数学与统计学院,安徽宿州234000

出　　处：《长春大学学报》2022年第8期8-15,共8页Journal of Changchun University

基　　金：安徽省高校自然科学研究项目(KJ2021ZD0136;KJ2021A1102);宿州学院重点科研项目(2020yzd06;2020BS011)。

摘　　要：五阶KdV方程主要用于模拟非线性色散波,如激光光学和等离子体物理在量子力学和非线性光学中有着广泛的应用。利用Tanh-coth法,得到了五阶KdV方程的行波解,再根据Riemann theta函数周期波解的方法,构造了五阶KdV方程的2-周期波解。借助数学软件Maple绘制了2-周期波解的传播形式的图,对周期波解和孤子解之间的关系做了分析,证明了参数在一定的极限条件下,周期波解趋近于孤子解。Fifth-order KdV equation is mainly used to simulate nonlinear dispersion waves, for example, laser optics and plasma physics have a wide application in quantum mechanics and nonlinear optics. The traveling wave solution of fifth-order KdV equation is obtained by means of Tanh-coth method, then 2-periodic wave solution of fifth-order KdV equation is constructed according to the method of periodic wave solution of Riemann theta function. The graph of propagation form of 2-periodic wave solution is drawn by the mathematical software Maple. The relationship between periodic wave solution and soliton solution is analyzed, and it is proved that periodic wave solution tends to the soliton solution under certain limit conditions.

关 键 词：五阶KDV方程 Tanh-coth法 行波解 Riemann theta函数 周期波解 渐近分析 

分 类 号：O175.29[理学—数学]