An Inverse Spectral Problem for a Special Class of Band Matrices and Bogoyavlensky Lattice

We study the inverse spectral problem method for one class of band matrices which can be applied to the integration (via Lax formalism) of Bogoyavlensky lattice in the finite case. Such matrices have a special structure which differs from the three-diagonal one of the matrices which appear in the La...

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Bibliographic Details
Published inRussian journal of mathematical physics Vol. 30; no. 1; pp. 96 - 110
Main Author Osipov, A. S.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.03.2023
Springer Nature B.V
Subjects
14/34
639/766/189
639/766/530
639/766/747
Algorithms
Inverse problems
Lattices
Mathematical and Computational Physics
Physics
Physics and Astronomy
Polynomials
Theoretical
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Summary:We study the inverse spectral problem method for one class of band matrices which can be applied to the integration (via Lax formalism) of Bogoyavlensky lattice in the finite case. Such matrices have a special structure which differs from the three-diagonal one of the matrices which appear in the Lax representation for Toda and Volterra lattices. The latter fact implies that the approach based upon the Shohat–Favard theorem and orthogonal polynomials is not applicable in this situation, as well as the use of the known continued fraction algorithms. However, it can be shown that the inverse spectral problem which amounts to reconstruction of the matrix from the moment sequence of its Weyl function, can be extended to our case. Also, the integration procedure for the finite non-Abelian Bogoyavlensky lattice by using this inverse problem method is offered.
ISSN:1061-9208
1555-6638
DOI:10.1134/S1061920823010065