Lucas polynomials and a standard Lax representation for the polytropic gas dynamics
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 nonstandard 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.
 Publication:

arXiv eprints
 Pub Date:
 October 2001
 arXiv:
 arXiv:hepth/0110097
 Bibcode:
 2001hep.th...10097C
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Number Theory;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 17 pages, LaTex