A Note on Fractional KdV Hierarchies

Abstract

We introduce a hierarchy of mutually commuting dynamical systems on a finite number of Laurent series. This hierarchy can be seen as a prolongation of the KP hierarchy, or a ``reduction'' in which the space coordinate is identified with an arbitrarily chosen time of a bigger dynamical system. Fractional KdV hierarchies are gotten by means of further reductions, obtained by constraining the Laurent series. The case of sl(3)^2 and its bihamiltonian structure are discussed in detail.

Final version to appear in J. Math. Phys. Some changes in the order of presentation, with more emphasis on the geometrical picture. One figure added (using epsf.sty). 30 pages, Latex

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• The Soliton Equations associated with the Affine Kac-Moody Lie Algebra G_2^{(1)}
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• Poisson pencils: reduction, exactness, and invariants
• Super KP equations and Darboux transformations: another perspective on the Jacobian Super KP hierarchy
• The Sato Grassmannian and the CH hierarchy