English

Linearization And Solutions Of The Discrete Painlev\'e-III Equation

solv-int 2009-10-22 v1 Exactly Solvable and Integrable Systems

Abstract

We present particular solutions of the discrete Painlev\'e III (d-PIII\rm_{III}) equation of rational and special function (Bessel) type. These solutions allow us to establish a close parallel between this discrete equation and its continuous counterpart. Moreover, we propose an alternate form for d-PIII\rm_{III} and confirm its integrability by explicitly deriving its Lax pair.

Keywords

Cite

@article{arxiv.solv-int/9310003,
  title  = {Linearization And Solutions Of The Discrete Painlev\'e-III Equation},
  author = {B. Grammaticos and F. W. Nijhoff and V. Papageorgiou and A. Ramani},
  journal= {arXiv preprint arXiv:solv-int/9310003},
  year   = {2009}
}