Construction of KdV Flow I.
τ-Function via Weyl Function

Shinichi Kotani

Osaka University, 2-13-2 Yurinokidai Sanda 669-1324, Japan
E-mail: skotani@outlook.com

Received February 6, 2018.

Abstract

Sato introduced the τ-function to describe solutions to a wide class of
completely integrable differential equations. Later Segal–Wilson represented
it in terms of the relevant integral operators on Hardy space of the unit
disc. This paper gives another representation of the τ -functions by the Weyl functions for 1d Schrödinger operators with real valued potentials, which will make it possible to extend the class of initial data for the KdV equation to more general one.