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Symmetries in the third Painlev\'e equation arising from the modified Pohlmeyer-Lund-Regge hierarchy

By Tetsuya Kikuchi

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.Comment: 23 page

Topics: Nonlinear Sciences - Exactly Solvable and Integrable Systems, Mathematical Physics
Year: 2011
DOI identifier: 10.1063/1.3658862
OAI identifier: oai:arXiv.org:1103.6075
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