Nonlocal Symmetries and Generation of Solutions for Partial Differential Equations
Copyright policy )Nonlocal Symmetries and Generation of Solutions for Partial Differential Equations
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/
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, Burgers equation, nonlocal symmetries, Invariance and symmetry properties for PDEs on manifolds, Mathematics - Analysis of PDEs, Reaction-diffusion equations, nonlinear heat equation, QA1-939, FOS: Mathematics, Nonlinear parabolic equations, Exactly Solvable and Integrable Systems (nlin.SI), Mathematics, Mathematical Physics, Geometric theory, characteristics, transformations in context of PDEs, Second-order nonlinear hyperbolic equations, Analysis of PDEs (math.AP)
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, Burgers equation, nonlocal symmetries, Invariance and symmetry properties for PDEs on manifolds, Mathematics - Analysis of PDEs, Reaction-diffusion equations, nonlinear heat equation, QA1-939, FOS: Mathematics, Nonlinear parabolic equations, Exactly Solvable and Integrable Systems (nlin.SI), Mathematics, Mathematical Physics, Geometric theory, characteristics, transformations in context of PDEs, Second-order nonlinear hyperbolic equations, Analysis of PDEs (math.AP)
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