On Partial Differential and Difference Equations with Symmetries Depending on Arbitrary Functions
Exactly Solvable and Integrable Systems
2015-12-08 v1 Mathematical Physics
math.MP
Abstract
In this note we present some ideas on when Lie symmetries, both point and generalized, can depend on arbitrary functions. We show on a few examples, both in partial differential and partial difference equations when this happens. Moreover we show that the infinitesimal generators of generalized symmetries depending on arbitrary functions, both for continuous and discrete equations, effectively play the role of master symmetries.
Cite
@article{arxiv.1512.01967,
title = {On Partial Differential and Difference Equations with Symmetries Depending on Arbitrary Functions},
author = {Giorgio Gubbiotti and Decio Levi and Christian Scimiterna},
journal= {arXiv preprint arXiv:1512.01967},
year = {2015}
}