Geodesic
The solution of Cauchy's problem for the Toda lattice with limit periodic initial data
Sbornik. Mathematics, Tome 199 (2008) no. 3, pp. 449-458

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Cauchy's problem for Toda lattices with initial data equal to the sum of a periodic and a rapidly decreasing sequence is solved with the use of the inverse scattering method. A method allowing one to find a limit periodic solution of the Toda lattice from a known periodic solution is described. The existence and uniqueness of a limit periodic solution is proved. Bibliography: 17 titles. 
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     author = {A. Kh. Khanmamedov},
     title = {The solution of {Cauchy's} problem for the {Toda} lattice with limit periodic initial data},
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A. Kh. Khanmamedov. The solution of Cauchy's problem for the Toda lattice with limit periodic initial data. Sbornik. Mathematics, Tome 199 (2008) no. 3, pp. 449-458. http://geodesic.mathdoc.fr/item/SM_2008_199_3_a5/