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 TMF, 2019, Volume 201, Number 1, Pages 37–53 (Mi tmf9728)

Some exact solutions of the Volterra lattice

V. E. Adler, A. B. Shabat

Landau Institute for Theoretical Physics, Chernogolovka, Moscow Oblast, Russia

Abstract: We study solutions of the Volterra lattice satisfying the stationary equation for its nonautonomous symmetry. We show that the dynamics in $t$ and $n$ are governed by the respective continuous and discrete Painlevé equations and describe the class of initial data leading to regular solutions. For the lattice on the half-axis, we express these solutions in terms of the confluent hypergeometric function. We compute the Hankel transform of the coefficients of the corresponding Taylor series based on the Wronskian representation of the solution.

Keywords: Volterra lattice, symmetry, Painlevé equation, confluent hypergeometric function, Hankel transformation, Catalan number.

 Funding Agency Grant Number Ministry of Science and Higher Education of the Russian Federation 0033-2019-0006 This research was performed under the State Assignment 0033-2019-0006 (Integrable systems of mathematical physics) of the Ministry of Science and Higher Education of the Russian Federation.

DOI: https://doi.org/10.4213/tmf9728

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English version:
Theoretical and Mathematical Physics, 2019, 201:1, 1442–1456

Bibliographic databases:

MSC: 37K10, 34M55, 33C15, 05A10
Revised: 28.03.2019

Citation: V. E. Adler, A. B. Shabat, “Some exact solutions of the Volterra lattice”, TMF, 201:1 (2019), 37–53; Theoret. and Math. Phys., 201:1 (2019), 1442–1456

Citation in format AMSBIB
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