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《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (4): 37-44.doi: 10.6040/j.issn.1671-9352.0.2018.110

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广义时变系数Gardner方程的Painlevé分析、李对称和精确解

王琪,李连忠*   

  1. 江南大学理学院, 江苏 无锡, 214122
  • 发布日期:2019-04-08
  • 作者简介:王琪(1994— ), 女, 硕士研究生, 研究方向为非线性偏微分方程及其精确解. E-mail:782512646@qq.com*通信作者简介:李连忠(1972— ), 男, 博士, 教授, 研究方向为非线性偏微分方程及其精确解. E-mail:llz3498@163.com
  • 基金资助:
    江苏省自然科学基金青年基金资助项目(BK20170171)

Painlevé analysis, Lie symmetry and exact solutions to the generalized time-dependent coefficients Gardner equation

WANG Qi, LI Lian-zhong*   

  1. School of Science, Jiangnan University, Wuxi 214122, Jiangsu, China
  • Published:2019-04-08

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摘要： 运用Painlevé分析与李对称分析得到该时变系数Gardner方程的可积条件及其在不同条件下的对称,并给出对应的动力学向量场,进而分别基于Painlevé分析和对称约化的思想,将时变系数Gardner方程转化为常系数方程,并结合幂级数法求解约化方程的精确解,得到时变系数Gardner方程的若干精确解。

关键词: Painlevé分析, 李对称分析, 对称约化, 幂级数解, 精确解

Abstract: A generalized Gardner equation with time-dependent coefficients is investigated in this paper, which arise in fluid dynamics, nonlinear lattice and plasma physics. By applying the combination of Painlevé analysis and Lie symmetry analysis method, the integrable conditions, symmetries and corresponding geometric vector fields of the time-dependent coefficient Gardner equation are investigated. Moreover, based on Painlevé analysis and the idea of symmetry reduction, the partial differential equations are reduced to ordinary differential equations. Combined with power series method, exact solutions to the reduced equations and a series of exact solutions to the original equations are obtained.

Key words: Painlevé analysis, Lie symmetry analysis, symmetry reduction, power series solution, exact solution

中图分类号: 

  • O175.2
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