F. Guil et M. Manas, AKNS HIERARCHY, SELF-SIMILARITY, STRING EQUATIONS AND THE GRASSMANNIAN, Journal of physics. A, mathematical and general, 27(6), 1994, pp. 2129-2142
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 thes
e 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 Nakam
ura-Hirota rational solutions of the NLS equation.