Discrete q-derivatives and symmetries of q-difference equations
Mathematical Physics
2009-11-10 v1 math.MP
Exactly Solvable and Integrable Systems
Abstract
In this paper we extend the umbral calculus, developed to deal with difference equations on uniform lattices, to q-difference equations. We show that many of the properties considered for shift invariant difference operators satisfying the umbral calculus can be implemented to the case of the q-difference operators. This q-umbral calculus can be used to provide solutions to linear q-difference equations and q-differential delay equations. To illustrate the method, we will apply the obtained results to the construction of symmetry solutions for the q-heat equation and to solve a linear ordinary second order q-difference equation
Keywords
Cite
@article{arxiv.math-ph/0310006,
title = {Discrete q-derivatives and symmetries of q-difference equations},
author = {D. Levi and J. Negro and M. A. del Olmo},
journal= {arXiv preprint arXiv:math-ph/0310006},
year = {2009}
}
Comments
23 pages, 17 figures, LaTex