Symmetries in the third Painlevé equation arising from the modified Pohlmeyer-Lund-Regge hierarchy

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 Painlevé equations. Especially, we present a new Lax representation and a complete description of the symmetry of the third Painlevé equation through the similarity reduction. We also show the relation between the tau-function of the mPLR hierarchy and Painlevé equations.

23 pages

References in corpus (1)

• On the Linearization of the Painleve' III-VI Equations and Reductions of the Three-Wave Resonant System

Cited by in corpus (1)

• The algebraic structure behind the derivative nonlinear Schroedinger equation