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.

• Березанський Юрій Макарович (1925–2019) (фізико-математичні науки)

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