Publication: AKNS hierarchy, self-similarity, string equations and the Grassmannian
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1994-03-21
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IOP Publishing LTD
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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 of the one-matrix model 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 by-product 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.
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©IOP Publishing LTD.
One of the authors (MM) is indebted to Dr.P.Guha for initial collaboration and to Prof.L.Bonora and Prof.G.Wilson for providing their papers.
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