Degeneracy of algebro geometric solutions of the Toda equation and Sato formulas
Résumé
We know that the degeneracy of solutions to PDE's given in terms of theta functions on Riemann surfaces gives important results about particular solutions as in the case of the NLS equation.
Here we degenerate the so called finite gap solutions of the Toda lattice equation from the general formulation in terms of abelian functions when the gaps tends to points. This degeneracy allows to recover the Sato formulas, without using inverse scattering theory or geometric or representation theoretic methods.
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