高阶变系数非线性发展方程的Painlev\'{e}&nbsp;分析

王媛

doi:10.13371/j.cnki.chin.q.j.m.2021.02.008

数学季刊 >

2021 , Vol. 36 >Issue 2: 196 - 203

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2021.02.008

高阶变系数非线性发展方程的Painlev\'{e} 分析

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Shanxi Institute of Energy

Wang Yuan (1986-), female, lecturer, engages in soliton theory and integrable system.

收稿日期: 2020-12-07

网络出版日期: 2021-01-18

基金资助

Supported by the Shanxi Education Department Project (Grant No. J2020398); Key Natural
Science Projects of Shanxi Energy Institute (Grant No. ZZ-2018003).

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Painlev\'{e} Analysis of Higher Order Nonlinear Evolution Equations with Variable Coefficients

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Shanxi Institute of Energy

Wang Yuan (1986-), female, lecturer, engages in soliton theory and integrable system.

Received date: 2020-12-07

Online published: 2021-01-18

Supported by

Supported by the Shanxi Education Department Project (Grant No. J2020398); Key Natural
Science Projects of Shanxi Energy Institute (Grant No. ZZ-2018003).

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摘要

There is a close relationship between the Painlev´e integrability and other
integrability of nonlinear evolution equation. By using the Weiss-Tabor-Carnevale (WTC)
method and the symbolic computation of Maple, the Painlev´e test is used for the higher
order generalized non-autonomous equation and the third order Korteweg-de Vries equation
with variable coefficients. Finally the Painlev´e integrability condition of this equation is
gotten.

关键词： Higher order generalized non-autonomous equation; Third order Korteweg-de
Vries equation with variable coefficients; Painlev′e analysis method

本文引用格式

王媛 . 高阶变系数非线性发展方程的Painlev\'{e} 分析[J]. 数学季刊, 2021 , 36(2) : 196 -203 . DOI: 10.13371/j.cnki.chin.q.j.m.2021.02.008

Abstract

Key words： Higher order generalized non-autonomous equation; Third order Korteweg-de
Vries equation with variable coefficients; Painlev′e analysis method

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