ON PARTIAL DIFFERENTIAL AND DIFFERENCE EQUATIONS WITH SYMMETRIES DEPENDING ON ARBITRARY FUNCTIONS

Authors

  • Giorgio Gubbiotti Dept. Math. Phys. Roma Tre University
  • Decio Levi Dip. Math. Phys. Roma Tre University
  • Christian Scimiterna Dept. Math. Phys. Roma Tre University

DOI:

https://doi.org/10.14311/AP.2016.56.0193

Keywords:

Lie point symmetries, generalized symmetries, partial differential equations, partial difference equations, Darboux integrable systems, linearizable nonlinear equations

Abstract

In this note we present some ideas on when Lie symmetries, both point and generalized, can depend on arbitrary functions. We show a few examples, both in partial differential and partial difference equations where 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.

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Published

2016-06-30

Issue

Vol. 56 No. 3 (2016)

Section

Articles

How to Cite

Gubbiotti, G., Levi, D., & Scimiterna, C. (2016). ON PARTIAL DIFFERENTIAL AND DIFFERENCE EQUATIONS WITH SYMMETRIES DEPENDING ON ARBITRARY FUNCTIONS. Acta Polytechnica, 56(3), 193-201. https://doi.org/10.14311/AP.2016.56.0193
Received 2015-12-06
Accepted 2016-03-08
Published 2016-06-30