منابع مشابه
The Toda Hierarchy and the Kdv Hierarchy
McKean and Trubowitz [2] showed that the theory of the KdV equation ∂ ∂t g(x, t) = ∂ 3 ∂x 3 g(x, t) − 6g(x, t) ∂g ∂x (x, t). is intimately related to the geometry of a related hyperelliptic curve of infinite genus, the Bloch spectrum B g t of the operator L g t : ψ → d 2 dx 2 ψ(x) + g(x, t)ψ(x), where g t = g(x, t). As was known classically, B g t is independent of t, when g(x, t) evolves accor...
متن کاملFunction of the Kdv Hierarchy
In this paper we construct a family of commuting multidimen-sional 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 hy-perelliptic curve to any solution of the stationary KdV equation. A basic generating function of the solutions ...
متن کاملFeynman Diagrams and the Kdv Hierarchy
The generating functional of the intersection numbers of the stable cohomology classes on moduli spaces of curves satisfy the string equation and a KdV hierarchy. We give a proof of this classical Kontsevich-Witten result completely in terms of Feynman diagrams.
متن کاملSELF - DUALITY AND THE KdV HIERARCHY
We derive the entire KdV hierarchy as well as the recursion relations from the self-duality condition on gauge fields in four dimensions.
متن کاملThe Kdv Hierarchy and Associated Trace Formulas
A natural algebraic approach to the KdV hierarchy and its algebro-geometric finite-gap solutions is developed. In addition, a new derivation of associated higher-order trace formulas in connection with one-dimensional Schrödinger operators is presented.
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 1996
ISSN: 0010-3616,1432-0916
DOI: 10.1007/bf02101288