Cubic and quartic transformations of the sixth Painleve equation in terms of Riemann-Hilbert correspondence

Details Cubic and quartic transformations of the sixth Painleve equation in terms of Riemann-Hilbert correspondence Cubic and quartic transformations of the sixth Painleve equation in terms of Riemann-Hilbert correspondence

2010-11-28

arxiv.org/abs/1011.6036v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Added: classification of quadratic transformations of the Monodromy manifold; new cubic (and quartic) transformations for Pica

Scientific paper

A starting point of this paper is a classification of quadratic polynomial transformations of the monodromy manifold for the 2x2 isomonodromic Fuchsian systems associated to the Painleve VI equation. Up to birational automorphisms of the monodromy manifold, we find three transformations. Two of them are identified as the action of known quadratic or quartic transformations of the Painleve VI equation. The third transformation of the monodromy manifold gives a new transformation of degree 3 of Picard's solutions of Painleve VI.

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