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Nonlocal Symmetries and Generation of Solutions for Partial Differential Equations

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 06 Feb 2007Embargo end date: 01 Jan 2007Publisher:SIGMA (Symmetry, Integrability and Geometry: Methods and Application)Journal:Symmetry, Integrability and Geometry: Methods and Applications (eissn: 1815-0659,

Authors: Tychynin, V.; Petrova, O.; Tertyshnyk, O.;

doi: 10.3842/sigma.2007.019 , 10.48550/arxiv.math-ph/0702033

arXiv: http://arxiv.org/abs/math-ph/0702033

Nonlocal Symmetries and Generation of Solutions for Partial Differential Equations

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Abstract

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.

Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

Related Organizations

Prydniprovs’ka State Academy of Civil Engineering and Architecture
Ukraine

Keywords

Lie classical symmetry, Nonlinear Sciences - Exactly Solvable and Integrable Systems, FOS: Physical sciences, Mathematical Physics (math-ph), formulae for generation of solutions, nonlinear superposition principle, nonlocal symmetries, Mathematics - Analysis of PDEs, QA1-939, FOS: Mathematics, Exactly Solvable and Integrable Systems (nlin.SI), Mathematics, Mathematical Physics, Analysis of PDEs (math.AP)

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