A new symmetry-based method for constructing nonlocally related PDE systems from admitted multi-parameter groups

Nonlocally related partial differential equation (PDE) systems can play an important role in the analysis of a given PDE system. In this paper, a new systematic method for obtaining nonlocally related PDE systems is developed. In particular, it is shown that if a PDE system admits q point symmetries...

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Bibliographic Details
Published in:Journal of mathematical physics 2020-06, Vol.61 (6)
Main Authors: Bluman, George W., de la Rosa, Rafael, Bruzón, María Santos, Gandarias, María Luz
Format: Article
Language:English
Subjects:
Algebra
Lie groups
Nonlinear equations
Partial differential equations
Physics
Reaction-diffusion equations
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Summary:Nonlocally related partial differential equation (PDE) systems can play an important role in the analysis of a given PDE system. In this paper, a new systematic method for obtaining nonlocally related PDE systems is developed. In particular, it is shown that if a PDE system admits q point symmetries whose infinitesimal generators form a q-dimensional solvable Lie algebra, then, for each resulting q-dimensional solvable algebra chain, one can obtain systematically q nonlocally related PDE systems. Such nonlocally related systems are obtained for a general class of nonlinear reaction–diffusion equations admitting two- to four-dimensional solvable algebras.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.5122319