Reduction of lattice equations to the Painlev\'e equations: P$_{\rm IV}$ and P$_{\rm V}$

Nobutaka Nakazono

arxiv: 1703.09215 · v3 · pith:2KZ7SZZTnew · submitted 2017-03-26 · 🌊 nlin.SI · math-ph· math.MP

Reduction of lattice equations to the Painlev\'e equations: P_(rm IV) and P_(rm V)

Nobutaka Nakazono This is my paper

classification 🌊 nlin.SI math-phmath.MP

keywords equationspainlevconstructconnectiondifference-differentialfifthfourthlattice

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In this paper, we construct a new relation between ABS equations and Painlev\'e equations. Moreover, using this connection we construct the difference-differential Lax representations of the fourth and fifth Painlev\'e equations.

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Reduction of lattice equations to the Painlev\'e equations: P_(rm IV) and P_(rm V)

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