Nonlocal Symmetries and Generation of Solutions for Partial Differential Equations

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dc.creatorTychynin, Valentyn
dc.creatorPetrova, Olga
dc.creatorTertyshnyk, Olesya
dc.date2007-02-09
dc.date.accessioned2026-07-07T09:34:27Z
dc.date.available2026-07-07T09:34:27Z
dc.descriptionWe 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.
dc.descriptionPublished in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
dc.identifierhttps://arxiv.org/abs/math-ph/0702033
dc.identifierhttp://arxiv.org/abs/math-ph/0702033
dc.identifierSIGMA 3 (2007), 019, 14 pages
dc.identifierdoi:10.3842/SIGMA.2007.019
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159497
dc.subjectMathematical Physics
dc.subjectAnalysis of PDEs
dc.subjectExactly Solvable and Integrable Systems
dc.titleNonlocal Symmetries and Generation of Solutions for Partial Differential Equations
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