2001/10/26 by Mikhail Kudryavtsev, Kudryavtsev, Mikhail
Mathematics · Physics and Astronomy · #34A12 #35G25 #Differential Equations and Boundary Problems #FOS: Mathematics #FOS: Physical sciences #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #math-ph #math.MP #math.SP #msc:34A12 #msc:35G25
paper · pdf · doi:10.48550/arxiv.math/0110293
18 pages
arxiv created 2001/10/26 · openalex publication_date 2001/10/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is the continuation of the work "On an inverse problem for finite-difference operators of second order". We consider the Cauchy problem for the Toda lattice in the case when the corresponding L-operator is a Jacobi matrix with bounded elements, whose spectrum of multipliciy 2 is separated from its simple spectrum and contains an interval of asolutely continuous spectrum. Using the integral equation of the inverse problem for this matrix, obtained in the previous work, we solve the Cauchy problem for the Toda lattice with non-stabilized initial data.