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.
Sufficient conditions for constructing a set of solutions of the Toda lattice are
analyzed. First, under certain conditions the invariance of the spectrum of is
established in the complex case. Second, given the tri-diagonal matrix defining a Toda lattice solution, the dynamic behavior of zeros of polynomials associated to 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.