$w$-function of the KdV hierarchy
Dynamical Systems
2007-05-23 v1
Abstract
In this paper we construct a family of commuting multidimensional differential 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 the stationary KdV equation. A basic generating function of the solutions of stationary KdV equation is introduced as a special polarization of the equation of the hyperelliptic curve. We also define and discuss the notion of a -function of a solution of the stationary -KdV equation.
Cite
@article{arxiv.math/0406457,
title = {$w$-function of the KdV hierarchy},
author = {V. M. Buchstaber and S. Yu. Shorina},
journal= {arXiv preprint arXiv:math/0406457},
year = {2007}
}