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- W1938746378 abstract "In the present paper we construct a family of differential commutingmultidimensional operators of order 3, which is closely related to the KdVhierarchy. We find a common eigenfunction of this family and an algebraicrelation between these operators. Using these operators we associate a hyperellipticcurve to any solution of stationary KdV equation. A basic generatingfunction of the solution of stationary KdV equation is introduced as specialpolarization of the hyperelliptic curve equation. The w-function is defined asa unique function with the following property: the second logarithmic derivativesof w are given by the basic generating function of the stationary g-KdVequation solution, in particular, the second logarithmic derivative of w withrespect to x gives this solution." @default.
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- W1938746378 date "2004-05-04" @default.
- W1938746378 modified "2023-10-16" @default.
- W1938746378 title "The 𝑤-function of the KdV hierarchy" @default.
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- W1938746378 doi "https://doi.org/10.1090/trans2/212/03" @default.
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