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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Official URL: http://www.ams.org/bookstore?co1=AND&co2=AND&co3=AND&d=BOOK&f=G&fn=105&l=100&op1=AND&op2=AND&op3=AND&p=1&pg1=&pg2=&pg3=ALLF&r=1&s1=&s2=&s3=volume%20212&subject=genint&u=

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.

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