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.

中文翻译：

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一种新的基于对称性的方法，用于从允许的多参数群构造非局部相关的偏微分方程系统

非局部相关偏微分方程 (PDE) 系统可以在给定 PDE 系统的分析中发挥重要作用。在本文中，开发了一种用于获得非局部相关 PDE 系统的新系统方法。特别地，它表明如果一个偏微分方程系统承认 q 点对称，其无穷小的发生器形成一个 q 维可解李代数，那么，对于每个产生的 q 维可解代数链，人们可以系统地获得 q 个非局部相关的 PDE 系统。这种非局部相关的系统是为一类允许二维到四维可解代数的非线性反应扩散方程获得的。