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Approximate solutions of nonlinear PDEs by the invariant expansion
  • ISSN号：1674-1056
  • 期刊名称：CHINESE PHYSICS B
  • 时间：2012.12
  • 页码：120204-
  • 分类：O175.29[理学—数学;理学—基础数学] O353.2[理学—流体力学;理学—力学]
  • 作者机构：[1]Faculty of Science, Ningbo University, Ningbo 315211, China, [2]Center of Nonlinear Science, Ningbo University, Ningbo 315211, China
  • 相关基金：Project supported by the National Natural Science Foundation of China （Grant No. 11175092）, Scientific Research Fund of Zhejiang Provincial Education Department （Grant No. Y201017148）, and K. C. Wong Magna Fund in Ningbo University.
  • 相关项目：达布变换，非局域对称及其局域化
作者： Wu Jiang-Long|Lou Sen-Yue*|
关键词： 非线性偏微分方程, BOUSSINESQ型方程, KDV-BURGERS方程, KORTEWEG-DE, 近似解, 非线性系统, KDV方程, 可积系统, approximate solution, invariant expansion, Mobious transformation invariance
中文摘要：

<正>It is difficult to obtain exact solutions of the nonlinear partial differential equations(PDEs) due to their complexity and nonlinearity,especially for non-integrable systems.In this paper,some reasonable approximations of real physics are considered,and the invariant expansion is proposed to solve real nonlinear systems.A simple invariant expansion with quite a universal pseudopotential is used for some nonlinear PDEs such as the Korteweg-de Vries(KdV) equation with a fifth-order dispersion term,the perturbed fourth-order KdV equation,the KdV-Burgers equation,and a Boussinesq-type equation.

英文摘要：

It is difficult to obtain exact solutions of the nonlinear partial differential equations （PDEs） due to their complexity and nonlinearity, especially for non-integrable systems. In this paper, some reasonable approximations of real physics are considered, and the invariant expansion is proposed to solve real nonlinear systems. A simple invariant expansion with quite a universal pseudopotential is used for some nonlinear PDEs such as the Korteweg-de Vries （KdV） equation with a fifth-order dispersion term, the perturbed fourth-order KdV equation, the KdV-Burgers equation, and a Boussinesq-type equation.

同期刊论文项目
达布变换，非局域对称及其局域化
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期刊信息
  • 《中国物理B：英文版》
  • 中国科技核心期刊
  • 主管单位:中国科学院
  • 主办单位:中国物理学会和中国科学院物理研究所
  • 主编：欧阳钟灿
  • 地址：北京 中关村 中国科学院物理研究所内
  • 邮编：100080
  • 邮箱：
  • 电话：010-82649026 82649519
  • 国际标准刊号：ISSN：1674-1056
  • 国内统一刊号：ISSN：11-5639/O4
  • 邮发代号:
  • 获奖情况:
  • 国内外数据库收录:
  • 被引量:406