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本文引用格式:杨先林,唐驾时.求一类非线性偏微分方程解析解的简洁构造算法[J].动力学与控制学报,2019,17(4):293~298;   Yang Xianlin,Tang Jiashi.A simple algorithm of contructing analytical solutions to a class of nonlinear partial differential equations[J].Journal of Dynamics and Control,2019,17(4):293-298.
求一类非线性偏微分方程解析解的简洁构造算法    点此下载全文
杨先林  唐驾时
湖南广播电视大学 理工部, 长沙 410004,湖南大学 机械与运载工程学院, 长沙 410082
基金项目:国家自然科学基金(11172093),国家开放大学科研项目(Q2705E)
DOI:10.6052/1672-6553-2019-023
摘要:
      通过引入一个变换,利用齐次平衡原理和选准一个待定函数来构造求解一类非线性偏微分方程解析解的算法.作为实例,我们将该算法应用到了mKdV方程,KdV-Burgers方程和KdV-Burgers-Kuramoto方程.借助符号计算软件Mathematica获得了这些方程的解析解.不难看出,该方法不仅简洁,而且有望进一步扩展.
关键词:非线性偏微分方程,解析解,mKdV方程,KdV-Burgers方程,KdV-Burgers Kuramoto方程
A simple algorithm of contructing analytical solutions to a class of nonlinear partial differential equations    Download Fulltext
Yang Xianlin  Tang Jiashi
Fund Project:
Abstract:
      By introducing a new transformation, using the principle of homogeneous balance and selecting an appropriate undetermined function, an algorithm was proposed to construct the analytical solutions to a class of nonlinear partial differential equations. As an example, this algorithm was applied to the mKdV equation,the KdV-Burgers equation and the KdV-Burgers-Kuramoto equation. Furthermore, the analytical solutions of such equations were obtained with the help of the symbolic computation system Mathematica. The results show that this algorithm is simple and effective to find out the analytical solutions of KdV equations, which could be extended to solve high-dimensional nonlinear partial differential equations.
Keywords:nonlinear partial differential equations,analytical solution,mKdV equation,KdV-Burgers equation,KdV-Burgers-Kuramoto equation
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