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 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. [ABSTRACT FROM AUTHOR]