Solutions to the Schrödinger equation with a Korteweg de Vries potential
Résumé
From the finite gap solutions of the KdV equation expressed in terms of abelian functions we construct solutions to the Schrödinger equation with a KdV potential in terms of fourfold Fredholm determinants. For this we establish a connection between Riemann theta functions and Fredholm determinants and we get multi-parametric solutions to this equation. As a consequence, a double wronskian representation of the solutions to this equation is constructed. We give also quasi rational solutions to this Schrödinger equation with rational KdV potentials.
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