Symmetries in the third Painlev\'e equation arising from the modified Pohlmeyer-Lund-Regge hierarchy
Exactly Solvable and Integrable Systems
2015-05-27 v1 Mathematical Physics
math.MP
Abstract
We propose a modification of the AKNS hierarchy that includes the "modified" Pohlmeyer-Lund-Regge (mPLR) equation. Similarity reductions of this hierarchy give the second, third, and fourth Painlev\'e equations. Especially, we present a new Lax representation and a complete description of the symmetry of the third Painlev\'e equation through the similarity reduction. We also show the relation between the tau-function of the mPLR hierarchy and Painlev\'e equations.
Keywords
Cite
@article{arxiv.1103.6075,
title = {Symmetries in the third Painlev\'e equation arising from the modified Pohlmeyer-Lund-Regge hierarchy},
author = {Tetsuya Kikuchi},
journal= {arXiv preprint arXiv:1103.6075},
year = {2015}
}
Comments
23 pages