应用(G'/G' + G + A)展开法求解mKdV方程的精确值解  

Applying the (G'/G' + G + A) Expansion Method to Solve the Exact Value Solution of mKdV Equation

作　　者：翁琨锋 邵廷朗 

机构地区：[1]广东财经大学统计与数学学院,广东 广州

出　　处：《应用数学进展》2024年第7期3301-3308,共8页Advances in Applied Mathematics

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。G'/G' + G + A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G'/G' + G + A展开法,运用行波变换,求解了mKdV方程,得到该方程的精确值解,并利用数学软件Maple画出了解的图像。As a model to describe the propagation of nonlinear waves in polar symmetric systems, mKdV equation is of great value to the study of wave problems in nonlinear optics. Further study of mKdV equation is beneficial to the solution of practical problems in physical optics, and the study of its solution method is of great significance. The G'/G' + G + A expansion method is an effective method for solving nonlinear partial differential equations based on the principle of homogeneous equilibrium developed in recent years. In this paper, mKdV equation is solved by using G'/G' + G + A expansion method and traveling wave transformation, and the exact value solution is obtained. Moreover, we use the mathematical software Maple to draw the understanding of the image.

关 键 词：MKDV方程 G'/G' + G + A展开法 行波变换 

分 类 号：O17[理学—数学]