## 2007.73: w-function of the KDV hierarchy

2007.73:
Victor Buchstaber and S. Yu. Shorina
(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 |
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Subjects: | MSC 2000 > 55 Algebraic topology |

MIMS number: | 2007.73 |

Deposited By: | Miss Louise Stait |

Deposited On: | 13 August 2007 |

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