Journal of Mathematical Physics, Analysis, Geometry
2018, vol. 14, No 3, pp. 297-335   https://doi.org/10.15407/mag14.03.297     ( to contents , go back )
https://doi.org/10.15407/mag14.03.297

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.

Mathematics Subject Classification 2000: 35Q53, 37K10, 35B15
Key words: KdV equation, Sato theory, Schrödinger operator.

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