On the Fay identity for KdV tau functions and the identity for the Wronskian of squared solutions of Sturm-Liouville equation

Abstract

We show that the well known identity for the Wronskian of squared solutions of a Sturm-Liouville equation follows from the Fay identity. We also study some odd-order (($2^n -1$)-order, $ n = 2, 3, ...$) identities which are specific for tau functions, related to the KdV hierarchy.