Heat Polynomials, Umbral Correspondence and Burgers Equations
Exactly Solvable and Integrable Systems
2007-05-23 v1
Abstract
We show that the umbral correspondence between differential equations can be achieved by means of a suitable transformation preserving the algebraic structure of the problems. We present the general properties of these transformations, derive explicit examples and discuss them in the case of the App\`{e}l and Sheffer polynomial families. We apply these transformations to non-linear equations, and discuss how the relevant solutions should be interpreted.
Keywords
Cite
@article{arxiv.nlin/0610076,
title = {Heat Polynomials, Umbral Correspondence and Burgers Equations},
author = {G. Dattoli and D. Levi},
journal= {arXiv preprint arXiv:nlin/0610076},
year = {2007}
}