The author earlier in [3, 4, 6, 7] proposed some way of integration the Cauchy problem for semi-infinite Toda lattices using the inverse spectral problem for Jacobi matrices. Such a way for double-infinite Toda lattices is more complicated and was proposed in [9]. This article is devoted to a detailed account of the result [3, 4, 6, 7, 9] . It is necessary to note that in the case of double-infinite lattices we cannot give a general solution of the corresponding linear system of differential equations for spectral matrix. Therefore, in this case the corresponding results can only be understood as a procedure of finding the solution of the Toda lattice.

Key words: Toda lattice, Cauchy problem, Jacobi and block Jacobi matrices, direct and inverse spectral problems, generalized eigenvector.

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Title

Linearization of double-infinite Toda lattice by means of inverse spectral problem

Yurij M. Berezansky, Linearization of double-infinite Toda lattice by means of inverse spectral problem, Methods Funct. Anal. Topology 18
(2012), no. 1, 19-54.

BibTex

@article {MFAT620,
AUTHOR = {Berezansky, Yurij M.},
TITLE = {Linearization of double-infinite Toda lattice by means of inverse spectral problem},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {18},
YEAR = {2012},
NUMBER = {1},
PAGES = {19-54},
ISSN = {1029-3531},
MRNUMBER = {MR2953329},
ZBLNUMBER = {1245.65131},
URL = {http://mfat.imath.kiev.ua/article/?id=620},
}