Noncommutative Toda Chains, Hankel Quasideterminants And Painlev'e II Equation

Abstract

We construct solutions of an infinite Toda system and an analogue of the Painlev'e II equation over noncommutative differential division rings in terms of quasideterminants of Hankel matrices.

16 pp; final revised version, will appear in J.Phys. A, minor changes (typos corrected following the Referee's List, aknowledgements and a new reference added)

References in corpus (2)

• On a direct approach to quasideterminant solutions of a noncommutative modified KP equation
• Quasideterminant solutions of a non-Abelian Hirota-Miwa equation

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• A fully noncommutative analog of the Painlevé IV equation and a structure of its solutions
• Soliton Scattering in Noncommutative Spaces
• Multi-Soliton Dynamics of Anti-Self-Dual Gauge Fields
• Non-Abelian Toda lattice and analogs of Painlevé III equation
• On classification of non-abelian Painlevé type systems
• Classification of Hamiltonian non-abelian Painlevé type systems
• Non-abelian Painlevé systems with generalized Okamoto integral
• Different linearizations of non-abelian second Painlevé systems and related monodromy surfaces