利用改进的Kudryashov方法求非线性偏微分方程的精确解  

Exact Solutions of Nonlinear Partial Differential Equation Using the Improved Kudryashov Method

作　　者：赵舒贤 欧耀骏 龙双英 李红春 ZHAO Shu-xian;OU Yao-Jun;LONG Shuang-ying;LI Hong-chun(College of Mathematics,Honghe University,Mengzi 661199,Yunnan,China)

机构地区：[1]红河学院数学与统计学院,云南蒙自661199

出　　处：《红河学院学报》2023年第5期138-144,共7页Journal of Honghe University

基　　金：国家级大学生创新创业项目(DCXI200152)。

摘　　要：非线性偏微分方程的求解在许多科学领域有重要作用.2012年,俄罗斯数学家Nikolay A.Kudryashov提出了一种新的方法,利用线性行波变换和辅助方程,可将所研究的非线性微分方程转化成常微分方程,既而实现计算的简化.改进的Kudryashov方法是在原方法的基础上改进了辅助方程,使得适用范围更加广泛.利用改进的Kudryashov方法求解六阶Boussinesq方程和空时分数阶Camassa-Holm方程,以这两个方程为例探究该方法在整数阶方程和分数阶方程中的应用.The solution of Nonlinear partial differential equation plays an important role in many scientific fields.In 2012,Russian mathematician Nikolay A.Kudryashov put forward a new method,which can transform the studied nonlinear differential equation into Ordinary differential equation by using linear traveling wave transform and auxiliary equation,thus simplifying the calculation.The improved Kudryashov method improves the auxiliary equation on the basis of the original method,making the application range more extensive.Using the improved Kudryashov method to solve the sixth order Boussinesq equation and the spatiotemporal fractional order Camassa Holm equation,explore the application of this method in integer and fractional order equations using these two equations as examples.

关 键 词：改进的Kudryashov方法 空时分数阶Camassa-Holm方程 六阶Boussinesq方程 精确解 

分 类 号：O172.1[理学—数学]