Nonlocal Symmetries and Generation of Solutions for Partial Differential Equations

被引：9

作者：

Tychynin, Valentyn ^{[1
]}

Petrova, Olga ^{[2
]}

Tertyshnyk, Olesya ^{[2
]}

机构：

[1] Prydniprovska State Acad Civil Engn & Architectur, UA-49005 Dnepropetrovsk, Ukraine

[2] Dnepropetrovsk Natl Univ, UA-49050 Dnepropetrovsk, Ukraine

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2007年 / 3卷

关键词：

Lie classical symmetry; nonlocal symmetries; formulae for generation of solutions; nonlinear superposition principle;

D O I：

10.3842/SIGMA.2007.019

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We have constructed new formulae for generation of solutions for the nonlinear heat equation and for the Burgers equation that are based on linearizing nonlocal transformations and on nonlocal symmetries of linear equations. Found nonlocal symmetries and formulae of nonlocal nonlinear superposition of solutions of these equations were used then for construction of chains of exact solutions. Linearization by means of the Legendre transformations of a second-order PDE with three independent variables allowed to obtain nonlocal superposition formulae for solutions of this equation, and to generate new solutions from group invariant solutions of a linear equation.

引用

页数：14

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