English

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.

Keywords

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}
}
R2 v1 2026-06-22T12:03:01.492Z