求一类非线性偏微分方程解析解的简洁构造算法
作者:
作者单位:

作者简介:

通讯作者:

中图分类号:

基金项目:

国家自然科学基金(11172093),国家开放大学科研项目(Q2705E)


A simple algorithm of contructing analytical solutions to a class of nonlinear partial differential equations
Author:
Affiliation:

Fund Project:

  • 摘要
  • |
  • 图/表
  • |
  • 访问统计
  • |
  • 参考文献
  • |
  • 相似文献
  • |
  • 引证文献
  • |
  • 资源附件
  • |
  • 文章评论
    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.

    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.

    参考文献
    相似文献
    引证文献
引用本文

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.

复制
分享
文章指标
  • 点击次数:
  • 下载次数:
  • HTML阅读次数:
  • 引用次数:
历史
  • 收稿日期:2017-03-08
  • 最后修改日期:2018-09-12
  • 录用日期:
  • 在线发布日期: 2019-08-26
  • 出版日期:

微信公众号二维码

手机版网站二维码