Guil Guerrero, Francisco JoséMañas Baena, Manuel Enrique2023-06-202023-06-201994-03-210305-447010.1088/0305-4470/27/6/034https://hdl.handle.net/20.500.14352/59704©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.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.engjournal articlehttp://dx.doi.org/10.1088/0305-4470/27/6/034http://iopscience.iop.orghttp://arxiv.org/abs/hep-th/9307017open access51-73Ordinary differential-equationsRational coefficientsTau-functionDeformationAlgebrasFísica-Modelos matemáticosFísica matemática