The relation between the Toda hierarchy and the KdV hierarchy
نویسندگان
چکیده
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...
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15 صفحه اولFunction 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 ...
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ژورنال
عنوان ژورنال: Physics Letters A
سال: 1999
ISSN: 0375-9601
DOI: 10.1016/s0375-9601(98)00886-x