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

F. Guil; M. Manas

doi:10.1088/0305-4470/27/6/034

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arXiv · hep-th/9307017

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

F. Guil·M. Manas

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Abstract

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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F. Guil, M. Manas. 1993-07-02. Akns Hierarchy, Self-Similarity, String Equations and the Grassmannian. https://doi.org/10.1088/0305-4470%2F27%2F6%2F034

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