Lucas polynomials and a standard Lax representation for the polytropic gas dynamics
High Energy Physics - Theory
2008-11-26 v1 Number Theory
Exactly Solvable and Integrable Systems
Abstract
A standard Lax representation for the polytropic gas dynamics is derived by exploiting various properties of the Lucas and Fibonacci polynomials. The two infinite sets of conserved charges are derived from this representation and shown to coincide with the ones derived from the known non-standard representation. The same Lax function is shown to also give the standard Lax description for the elastic medium equations. In addition, some results on possible dispersive extensions of such models are presented.
Cite
@article{arxiv.hep-th/0110097,
title = {Lucas polynomials and a standard Lax representation for the polytropic gas dynamics},
author = {A. Constandache and Ashok Das and F. Toppan},
journal= {arXiv preprint arXiv:hep-th/0110097},
year = {2008}
}
Comments
17 pages, LaTex