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Surfaces de Bonnet et \'equations de Painlev\'e

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arxiv 1607.01222 v2 pith:4XTBAZ4Q submitted 2016-07-05 math-ph math.DGmath.MPnlin.SI

Surfaces de Bonnet et \'equations de Painlev\'e

Robert Conte (ENS Cachan , CNRS , Universit\'e Paris-Saclay , France) This is my paper
classification math-ph math.DGmath.MPnlin.SI
keywords bonnetequationspainlevsurfacesequationconduisentdeuxextrapolated
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Nous montrons que les \'equations du rep\`ere mobile des surfaces de Bonnet conduisent \`a une paire de Lax matricielle isomonodromique d'ordre deux pour la sixi\`eme \'equation de Painlev\'e. We show that the moving frame equations of Bonnet surfaces can be extrapolated to a second order, isomonodromic matrix Lax pair of the sixth Painlev\'e equation.

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  1. Geometry of the Ising persistence problem and the universal Bonnet-Manin Painlev\'e VI distribution

    math-ph 2026-03 conditional novelty 7.0

    The full persistence distribution in 1D Ising coarsening equals a Pfaffian Fredholm determinant of the sech kernel and is controlled by a Painlevé VI equation that is the mean curvature of a Bonnet surface.