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

E. K. Ifantis, K. N. Vlachou
2004 Abstract and Applied Analysis  
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 measureμ, the solutionαn(t),bn(t)of the Toda lattice is exactly determined and by takingt=0, the solutionαn(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 everyt>0and can also be obtained from the solutions of a simple
more » ... of a simple differential equation. Many other exact solutions obtained from this differential equation show that there exist initial conditionsαn(0)>0andbn(0)∈ℝsuch that the semi-infinite Toda lattice is not integrable in the sense that the functionsαn(t)andbn(t)are not finite for everyt>0.
doi:10.1155/s1085337504306135 fatcat:gmea44bd35a3heezqpiw3so6kq