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 Zh. Mat. Fiz. Anal. Geom., 2018, Volume 14, Number 3, Pages 297–335 (Mi jmag702)

Construction of KdV flow I. $\tau$-Function via Weyl function

S. Kotani

Osaka University, 2-13-2 Yurinokidai Sanda 669-1324, Japan

Abstract: Sato introduced the $\tau$-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 $\tau$-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.

Key words and phrases: KdV equation, Sato theory, Schrödinger operator.

 Funding Agency Grant Number Japan Society for the Promotion of Science 26400128 The author is partly supported by JSPS KAKENHI Grant Number 26400128.

DOI: https://doi.org/10.15407/mag14.03.297

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MSC: 35Q53, 37K10, 35B15
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Citation: S. Kotani, “Construction of KdV flow I. $\tau$-Function via Weyl function”, Zh. Mat. Fiz. Anal. Geom., 14:3 (2018), 297–335

Citation in format AMSBIB
\Bibitem{Kot18} \by S.~Kotani \paper Construction of KdV flow~I. $\tau$-Function via Weyl function \jour Zh. Mat. Fiz. Anal. Geom. \yr 2018 \vol 14 \issue 3 \pages 297--335 \mathnet{http://mi.mathnet.ru/jmag702} \crossref{https://doi.org/10.15407/mag14.03.297} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000450683100004}