منابع مشابه
From Toda to KdV
For periodic Toda chains with a large number N of particles we consider states which are N−2-close to the equilibrium and constructed by discretizing arbitrary given C2−functions with mesh size N−1. Our aim is to describe the spectrum of the Jacobi matrices LN appearing in the Lax pair formulation of the dynamics of these states as N → ∞. To this end we construct two Hill operators H± – such op...
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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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We give a gauge invariant formulation of N = 2 supersymmetric abelian Toda field equations in N = 2 superspace. Superconformal invariance is studied. The conserved currents are shown to be associated with Drinfeld-Sokolov type gauges. The extension to non-abelian N = 2 Toda equations is discussed. Very similar methods are then applied to a matrix formulation in N = 2 superspace of one of the N ...
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The goal of this crash course is to make a brief introduction into the beautiful world of integrable hierarchies. We do not intend to give a general survey of integrable system theory but rather want to use few known examples to introduce notions and initial circle of ideas specific for integrable equations. We used [A] as a reference for the first section, [P] for the second section, and [MJD]...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 2003
ISSN: 0022-040X
DOI: 10.4310/jdg/1090426941