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