Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 237487, 12 pages
doi:10.1155/2009/237487
Research Article

Spectrum and Generation of Solutions of the Toda Lattice

D. Barrios Rolanía1 and J. R. Gascón Márquez2

1Facultad de Informática, Universidad Politécnica de Madrid, 28660 Madrid, Spain
2Área de Matemática, Universidad Nacional Abierta, 1010 Caracas, Venezuela

Received 8 July 2009; Accepted 22 September 2009

Academic Editor: Manuel De la Sen

Copyright © 2009 D. Barrios Rolanía and J. R. Gascón Márquez. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Sufficient conditions for constructing a set of solutions of the Toda lattice are analyzed. First, under certain conditions the invariance of the spectrum of J(t) is established in the complex case. Second, given the tri-diagonal matrix J(t) defining a Toda lattice solution, the dynamic behavior of zeros of polynomials associated to J(t) is analyzed. Finally, it is shown by means of an example how to apply our results to generate complex solutions of the Toda lattice starting with a given solution.