Symmetries of differential ideals and differential equations

Oleg V. Kaptsov

Institute of Computational Modelling SD RAS, Academgorodok, 50/44, Krasnoyarsk, 660036, Russia

Abstract: The paper deals with differential rings and partial differential equations with coefficients in some algebra. We introduce symmetries and the conservation laws to the differential ideal of an arbitrary differential ring. We prove that a set of symmetries of an ideal forms a Lie ring and give a precise criterion when a differentiation is a symmetry of an ideal. These concepts are applied to partial differential equations.

Keywords: differential rings, symmetry, partial differential equations.

UDC: 519.21

Received: 28.12.2018
Received in revised form: 11.01.2019
Accepted: 06.02.2019

Language: English

DOI: 10.17516/1997-1397-2018-12-2-185-190

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