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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2021. Vol 38

On the Construction and Integration of a Hierarchy for the Periodic Toda Lattice with a Self-Consistent Source

Author(s)

B. A. Babajanov, M. M. Ruzmetov

Abstract

In this paper, it is derived a rich hierarchy for the Toda lattice with a selfconsistent source in the class of periodic functions. We discuss the complete integrability of the constructed systems that is based on the transformation to the spectral data of an associated discrete Hill‘s equation with periodic coefficients. In particular, Dubrovintype equations are derived for the time-evolution of the spectral data corresponding to the solutions of any system in the hierarchy. At the end of the paper, we illustrate our theory on concrete example with analytical and numerical results.

About the Authors

Bazar Babajanov, Dr. Sci. (Phys.–Math.), Assoc. Prof., Urgench State University, 14, Kh. Alimdjan st., Urgench, 220100, Republic of Uzbekistan, tel.:+9(9862)224-67-00, email: a.murod@mail.ru

Murod Ruzmetov, Senior Lecturer, Urgench State University, 14, Kh. Alimdjan st., Urgench, 220100, Republic of Uzbekistan, tel.:+9(9862)224-67-00, email: rmurod2002@gmail.com

For citation

Babajanov B.A., Ruzmetov M.M. On the Construction and Integration of a Hierarchy for the Periodic Toda Lattice with a Self-Consistent Source. The Bulletin of Irkutsk State University. Series Mathematics, 2021, vol. 38, pp. 3-18. https://doi.org/10.26516/1997-7670.2021.38.3

Keywords
periodic Toda lattice hierarchy, Hill’s equation, self-consistent source, inverse spectral problem, trace formulas.
UDC
517.95
MSC
35Q51
DOI
https://doi.org/10.26516/1997-7670.2021.38.3
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