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Symmetry, Integrability and Geometry: Methods and Applications, 2007, Volume 3, 019, 14 pp.
DOI: https://doi.org/10.3842/SIGMA.2007.019 (Mi sigma145) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Nonlocal Symmetries and Generation of Solutions for Partial Differential Equations

Valentyn Tychynina, Olga Petrovab, Olesya Tertyshnykb

a Prydniprovs'ka State Academy of Civil Engineering and Architecture, 24a Chernyshevsky Str., Dnipropetrovsk, 49005 Ukraine
b Dnipropetrovsk National University, 13 Naukovyi Per., Dnipropetrovsk, 49050 Ukraine
Full-text PDF (254 kB) Citations (9)
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DOI: https://doi.org/10.3842/SIGMA.2007.019
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.
Keywords: Lie classical symmetry; nonlocal symmetries; formulae for generation of solutions; nonlinear superposition principle.
Received: January 6, 2006; in final form January 17, 2007; Published online February 6, 2007
Bibliographic databases:
Document Type: Article
MSC: 35A30; 35K55; 35K57; 35L70
Language: English
Citation: Valentyn Tychynin, Olga Petrova, Olesya Tertyshnyk, “Nonlocal Symmetries and Generation of Solutions for Partial Differential Equations”, SIGMA, 3 (2007), 019, 14 pp.
Citation in format AMSBIB
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\by Valentyn Tychynin, Olga Petrova, Olesya Tertyshnyk
\paper Nonlocal Symmetries and Generation of Solutions for Partial Differential Equations
\jour SIGMA
\yr 2007
\vol 3
\papernumber 019
\totalpages 14
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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