%0 Journal Article
%A Guil Guerrero, Francisco José
%A Mañas Baena, Manuel Enrique
%T AKNS hierarchy, self-similarity, string equations and the Grassmannian
%D 1994
%@ 0305-4470
%U https://hdl.handle.net/20.500.14352/59704
%X 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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