Nonlocal Symmetries and Generation of Solutions for Partial Differential Equations

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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/

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Mathematical Physics, Analysis of PDEs, Exactly Solvable and Integrable Systems

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http://salesiana.dossiersoluciones.com/handle/123456789/159497

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math-ph/0702033
 http://arxiv.org/abs/math-ph/0702033
 SIGMA 3 (2007), 019, 14 pages
 doi:10.3842/SIGMA.2007.019

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arXiv