Resolution of the Cauchy problem for the Toda lattice with non-stabilized initial data

Details Resolution of the Cauchy problem for the Toda lattice with non-stabilized initial data Resolution of the Cauchy problem for the Toda lattice with non-stabilized initial data

2001-10-26

arxiv.org/abs/math/0110293v1

Mathematics

Spectral Theory

18 pages

Scientific paper

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.

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