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13 May 2004 Exact solutions of the semi-infinite Toda lattice with applications to the inverse spectral problem
E. K. Ifantis, K. N. Vlachou
Abstr. Appl. Anal. 2004(5): 435-451 (13 May 2004). DOI: 10.1155/S1085337504306135

Abstract

Several inverse spectral problems are solved by a method which is based on exact solutions of the semi-infinite Toda lattice. In fact, starting with a well-known and appropriate probability measure μ, the solution αn(t), bn(t) of the Toda lattice is exactly determined and by taking t=0, the solution αn(0), bn(0) of the inverse spectral problem is obtained. The solutions of the Toda lattice which are found in this way are finite for every t>0 and can also be obtained from the solutions of a simple differential equation. Many other exact solutions obtained from this differential equation show that there exist initial conditions αn(0)>0 and bn(0) such that the semi-infinite Toda lattice is not integrable in the sense that the functions αn(t) and bn(t) are not finite for every t>0.

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E. K. Ifantis. K. N. Vlachou. "Exact solutions of the semi-infinite Toda lattice with applications to the inverse spectral problem." Abstr. Appl. Anal. 2004 (5) 435 - 451, 13 May 2004. https://doi.org/10.1155/S1085337504306135

Information

Published: 13 May 2004
First available in Project Euclid: 1 June 2004

zbMATH: 1070.37054
MathSciNet: MR2063337
Digital Object Identifier: 10.1155/S1085337504306135

Subjects:
Primary: 34A55 , 37K10
Secondary: 37L60

Rights: Copyright © 2004 Hindawi

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Vol.2004 • No. 5 • 13 May 2004
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