From Algebro Geometric Solutions of the Toda Equation to Sato Formulas

Abstract

We know that the degeneracy of solutions to PDEs, given in terms of theta functions on Riemann surfaces, provides 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 tend to points. This degeneracy allows us to recover the Sato formulas without using inverse scattering theory or geometric or representation theoretic methods.

Keywords

• Riemann surfaces
• theta functions
• abelian integrals
• Baker Akhiezer functions
• Sato formulas