This article is cited in 3 papers

Subsymmetries and their properties

V. Rosenhaus^a, R. Shankar<sup>b

a</sup> Department of Mathematics and Statistics, California State University, Chico, CA, USA
^b Department of Mathematics, University of Washington, Seattle, WA, USA

Abstract: We introduce a subsymmetry of a differential system as an infinitesimal transformation of a subset of the system that leaves the subset invariant on the solution set of the entire system. We discuss the geometric meaning and properties of subsymmetries and also an algorithm for finding subsymmetries of a system. We show that a subsymmetry is a significantly more powerful tool than a regular symmetry with regard to deformation of conservation laws. We demonstrate that all lower conservation laws of the nonlinear telegraph system can be generated by system subsymmetries.

Keywords: symmetry, symmetry extension, differential system, invariance property.

PACS: 02.30.Jr, 02.20.Sv

MSC: 22E70, 35Qxx

Received: 08.08.2017
Revised: 01.11.2017

DOI: 10.4213/tmf9440

 English version: Theoretical and Mathematical Physics, 2018, 197:1, 1514–1526

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