Spectrum and Generation of Solutions of the Toda Lattice - D. Barrios Rolanía; J. R. Gascón Márquez (Discrete Dynamics in Nature and Society)
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.