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

E. K. Ifantis and K. N. Vlachou

Abstract and Applied Analysis, 2004, vol. 2004, 1-17

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 α n ( t ) , b n ( t ) of the Toda lattice is exactly determined and by taking t = 0 , the solution α n ( 0 ) , b n ( 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 α n ( 0 ) > 0 and b n ( 0 ) ∈ ℝ such that the semi-infinite Toda lattice is not integrable in the sense that the functions α n ( t ) and b n ( t ) are not finite for every t > 0 .

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:928347

DOI: 10.1155/S1085337504306135

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