Nonlocal Symmetries and Generation of Solutions for Partial Differential Equations

Details Nonlocal Symmetries and Generation of Solutions for Partial Differential Equations Nonlocal Symmetries and Generation of Solutions for Partial Differential Equations

2007-02-09

arxiv.org/abs/math-ph/0702033v1

SIGMA 3 (2007), 019, 14 pages

Physics

Mathematical Physics

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

Scientific paper

10.3842/SIGMA.2007.019

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.

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