Some exact solutions of the Volterra lattice

DOI10.1134/S0040577919100039zbMath1440.37071arXiv1903.11901OpenAlexW3098433588WikidataQ126836010 ScholiaQ126836010MaRDI QIDQ2174677

A. B. Shabat, Vsevolod Eduardovich Adler

Publication date: 21 April 2020

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.11901

zbMATH Keywords

symmetryCatalan numberPainlevé equationconfluent hypergeometric functionHankel transformationVolterra lattice

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15) Lattice dynamics; integrable lattice equations (37K60) Integrable difference and lattice equations; integrability tests (39A36)

Related Items (4)

On the problem of classifying integrable chains with three independent variables ⋮ Bogoyavlensky lattices and generalized Catalan numbers ⋮ Invariant manifolds and separation of the variables for integrable chains ⋮ Painlevé type reductions for the non-Abelian Volterra lattices ^*

Cites Work

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• Symmetry approach to the integrability problem
• Master symmetries for differential-difference equations of the Volterra type
• On the complete integrability of a nonlinear system of partial differential equations in two-dimensional space
• Discrete Painlevé equations and their appearance in quantum gravity
• Catalan-like numbers and determinants
• The Hankel Determinant of Exponential Polynomials
• The isomonodromy approach in the theory of two-dimensional quantum gravitation
• From continuous Painlevé IV to the asymmetric discrete Painlevé I

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