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arXiv · 1103.6075

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

Tetsuya Kikuchi
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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.

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Tetsuya Kikuchi. 2011-03-31. Symmetries in the third Painlevé equation arising from the modified Pohlmeyer-Lund-Regge hierarchy. https://doi.org/10.1063/1.3658862

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