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arXiv · 1509.05101

Sub-symmetries I. Main properties and applications

V. Rosenhaus·Ravi Shankar
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Abstract

We introduce a sub-symmetry 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 geometrical meaning and properties of sub-symmetries, as well as an algorithm for finding sub-symmetries of a system. We show some of the benefits of using sub-symmetries in the search for solutions of a system; in particular , we show how sub-symmetries can be used in decoupling a differential system. We also discuss the role of sub-symmetries in the deformation of known conservation laws of a system into other (often, new) conservation laws and show that, in this regard, a sub-symmetry is a considerably more powerful tool than a regular symmetry. We demonstrate that all lower conservation laws of the nonlinear telegraph system can be generated by sub-symmetries.

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V. Rosenhaus, Ravi Shankar. 2015-09-17. Sub-symmetries I. Main properties and applications. https://arxiv.org/abs/1509.05101

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