一类mKdV方程的孤立波解  

Solitary Wave Solutions for a Class of mKdV Equations

作　　者：陆求赐[1] 张宋传 王学彬[2] LU Qiuci;ZHANG Songchuan;WANG Xuebin(College of Humanities and teachers education,,Wuyi University,Wuyishan 354300,China;College of Mathematics and computer,Wuyi University,Wuyishan,354300,China)

机构地区：[1]武夷学院人文与教师教育学院,福建武夷山354300 [2]武夷学院数计学院,福建武夷山354300

出　　处：《中央民族大学学报（自然科学版）》2021年第2期5-11,共7页Journal of Minzu University of China(Natural Sciences Edition)

基　　金：福建省自然科学基金(2017J01769);福建省教育厅科技项目(JA15512、JAT160519);高级引进人才科研启动基金(YJ201802)。

摘　　要：作为一个描述非线性波在具有极性对称性的系统中传播的模型,mKdV方程对于研究非线性光学中的波动问题等有重要的价值,对其作深入研究有利于物理光学中实际问题的解决,其求解方法的研究有着重要的意义,1/G展开法是近年来发展起来的基于齐次平衡原理的求解非线性偏微分方程的一种较为有效的方法。本文利用1/G展开法求解了一类mKdV方程,得到了孤立波解和扭曲波解,并利用数学软件画出了解的图像,同时对解的图像的结构和变化趋势作了简要的分析。The mKdV equation is a model to describe the propagation of nonlinear waves in a systems with polar symmetry,it plays an important role in the research of wave problems in nonlinear optics,a deep research of m KdV equations is beneficial to solve practical problems in physical optics.It is of great significance to the research of the solving methods of mKdV equation.The 1/G expansion method is an effective method for solving nonlinear partial differential equations based on homogeneous equilibrium principle which has been developed in recent years.In this paper,we use the 1/G expansion method to solve a class of mKdV equations,and obtain solitary and distorted wave solutions.Then we draw the image of the solution by using mathematical software,at the same time,we analyze the structure and changing trend of the image briefly.

关 键 词：MKDV方程 1/G展开法 行波变换 孤立波解 扭曲波解 

分 类 号：O175.26[理学—数学]