Abstract
Nonlocally related partial differential equation (PDE) systems are important in the analysis of a given PDE system. In particular, they are useful for seeking nonlocal symmetries. It is known that each local conservation law of a given PDE system systematically yields a nonlocally related PDE system. In this paper, a new and complementary method for constructing nonlocally related PDE systems is introduced. In particular, it is shown that each point symmetry of a PDE system systematically yields a nonlocally related PDE system. Examples include nonlinear reaction-diffusion equations, nonlinear diffusion equations, and nonlinear wave equations. The considered nonlinear reaction-diffusion equations have no local conservation laws. Previously unknown nonlocal symmetries are exhibited through our new symmetry-based method for two examples of nonlinear wave equations.
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