Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2004, Number 5 (2004), 435-451.
Exact solutions of the semi-infinite Toda lattice with applications to the inverse spectral problem
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 , the solution , of the Toda lattice is exactly determined and by taking , the solution , of the inverse spectral problem is obtained. The solutions of the Toda lattice which are found in this way are finite for every 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 and such that the semi-infinite Toda lattice is not integrable in the sense that the functions and are not finite for every .
Abstr. Appl. Anal., Volume 2004, Number 5 (2004), 435-451.
First available in Project Euclid: 1 June 2004
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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