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arXiv · 1211.0100

A Symmetry-Based Method for Constructing Nonlocally Related PDE Systems

George W. Bluman·Zhengzheng Yang
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Abstract

Nonlocally related partial differential equation (PDE) systems are useful in the analysis of a given PDE system. It is known that each local conservation law of a given PDE system systematically yields a nonlocally related system. In this paper, a new and complementary method for constructing nonlocally related systems is introduced. In particular, it is shown that each point symmetry of a given PDE system systematically yields a nonlocally related system. Examples include applications to nonlinear diffusion equations, nonlinear wave equations and nonlinear reaction-diffusion equations. As a consequence, previously unknown nonlocal symmetries are exhibited for two examples of nonlinear wave equations. Moreover, since the considered nonlinear reaction-diffusion equations have no local conservation laws, previous methods do not yield nonlocally related systems for such equations.

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George W. Bluman, Zhengzheng Yang. 2012-11-01. A Symmetry-Based Method for Constructing Nonlocally Related PDE Systems. https://doi.org/10.1063/1.4819724

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