Symmetries of linear and nonlinear partial differential equations

2024/05/28 by О. В. Капцов, Kaptsov, Oleg
Mathematics · Engineering · Physics and Astronomy · #Numerical methods for differential equations #Dynamics and Control of Mechanical Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2405.17973

Abstract

We consider higher symmetries and operator symmetries of linear partial differential equations. The higher symmetries form a Lie algebra, and operator ones form an associative algebra. The relationship between these symmetries is established. We show that symmetries of linear equations sometimes generate symmetries of nonlinear ones. New symmetries of two-dimensional stationary equations of gas dynamics are found.

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