w-function of the KDV hierarchy

Buchstaber, Victor and Shorina, S. Yu. (2004) w-function of the KDV hierarchy. Geometry, Topology and Mathematical Physics, 212. pp. 41-46. ISSN 0065-9290

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Abstract

In the present paper we construct a family of differential commuting multidimensional operators of order 3, which is closely related to the KdV hierarchy. We find a common eigenfunction of this family and an algebraic relation between these operators. Using these operators we associate a hyperelliptic curve to any solution of stationary KdV equation. A basic generating function of the solution of stationary KdV equation is introduced as special polarization of the hyperelliptic curve equation. The w-function is defined as a unique function with the following property: the second logarithmic derivatives of w are given by the basic generating function of the stationary g-KdV equation solution, in particular, the second logarithmic derivative of w with respect to x gives this solution.

Item Type:	Article
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 55 Algebraic topology
Depositing User:	Ms Lucy van Russelt
Date Deposited:	13 Aug 2007
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/764

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