Akns Hierarchy, Self-Similarity, String Equations and the Grassmannian

Details Akns Hierarchy, Self-Similarity, String Equations and the Grassmannian Akns Hierarchy, Self-Similarity, String Equations and the Grassmannian

1993-07-02

arxiv.org/abs/hep-th/9307017v1

J.Phys. A27 (1994) 2129-2142

Physics

High Energy Physics

High Energy Physics - Theory

25 pages in AMS-LaTeX

Scientific paper

10.1088/0305-4470/27/6/034

In this paper the Galilean, scaling and translational self--similarity conditions for the AKNS hierarchy are analysed geometrically in terms of the infinite dimensional Grassmannian. The string equations found recently by non--scaling limit analysis of the one--matrix model are shown to correspond to the Galilean self--similarity condition for this hierarchy. We describe, in terms of the initial data for the zero--curvature 1--form of the AKNS hierarchy, the moduli space of these self--similar solutions in the Sato Grassmannian. As a byproduct we characterize the points in the Segal--Wilson Grassmannian corresponding to the Sachs rational solutions of the AKNS equation and to the Nakamura--Hirota rational solutions of the NLS equation. An explicit 1--parameter family of Galilean self--similar solutions of the AKNS equation and the associated solution to the NLS equation is determined.

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