Reduction operators of Burgers equation

被引：8

作者：

Pocheketa, Oleksandr A. ^{[1
]}

Popovych, Roman O. ^{[1
,2
]}

机构：

[1] NAS Ukraine, Inst Math, UA-01601 Kiev, Ukraine

[2] Univ Vienna, Fac Math, A-1090 Vienna, Austria

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2013年 / 398卷 / 01期

基金：

奥地利科学基金会;

关键词：

Burgers equation; Nonclassical symmetry; Reduction operator; Lie symmetry; Exact solution; PARTIAL-DIFFERENTIAL-EQUATIONS; SIMILARITY REDUCTIONS; HEAT-EQUATION; CONDITIONAL SYMMETRIES; BOUSSINESQ EQUATION; EVOLUTION-EQUATIONS;

D O I：

10.1016/j.jmaa.2012.08.062

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The solution of the problem on reduction operators and nonclassical reductions of the Burgers equation is systematically treated and completed. A new proof of the theorem on the special "no-go" case of regular reduction operators is presented, and the representation of the coefficients of operators in terms of solutions of the initial equation is constructed for this case. All possible nonclassical reductions of the Burgers equation to single ordinary differential equations are exhaustively described. Any Lie reduction of the Burgers equation proves to be equivalent via the Hopf-Cole transformation to a parameterized family of Lie reductions of the linear heat equation. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：270 / 277

页数：8