Abstract and Applied Analysis

Exact solutions of the semi-infinite Toda lattice with applications to the inverse spectral problem

E. K. Ifantis and K. N. Vlachou

Full-text: Open access

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.

Article information

Source
Abstr. Appl. Anal., Volume 2004, Number 5 (2004), 435-451.

Dates
First available in Project Euclid: 1 June 2004

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1086103974

Digital Object Identifier
doi:10.1155/S1085337504306135

Mathematical Reviews number (MathSciNet)
MR2063337

Zentralblatt MATH identifier
1070.37054

Subjects
Primary: 34A55: Inverse problems 37K10
Secondary: 37L60

Citation

Ifantis, E. K.; Vlachou, K. N. Exact solutions of the semi-infinite Toda lattice with applications to the inverse spectral problem. Abstr. Appl. Anal. 2004 (2004), no. 5, 435--451. doi:10.1155/S1085337504306135. https://projecteuclid.org/euclid.aaa/1086103974


Export citation