Scaling Self-Similar Formulation of the String Equations of the Hermitian Matrix Model

Abstract

The string equation appearing in the double scaling limit of the Hermitian one--matrix model, which corresponds to a Galilean self--similar condition for the KdV hierarchy, is reformulated as a scaling self--similar condition for the Ur--KdV hierarchy. A non--scaling limit analysis of the one--matrix model has led to the complexified NLS hierarchy and a string equation. We show that this corresponds to the Galilean self--similarity condition for the AKNS hierarchy and also its equivalence to a scaling self--similar condition for the Heisenberg ferromagnet hierarchy.

12 pages in AMS-LaTeX, AMS-LaTeXable version

References in corpus (4)

• Matrix models without scaling limit
• An alternative approach to KP hierarchy in matrix models
• Akns Hierarchy, Self-Similarity, String Equations and the Grassmannian
• String Equations for the Unitary Matrix Model and the Periodic Flag Manifold