The matrix-resolvent method to tau-functions for the nonlinear Schrödinger hierarchy

Abstract

We extend the matrix-resolvent method of computing logarithmic derivatives of tau-functions to the nonlinear Schrödinger (NLS) hierarchy. Based on this method we give a detailed proof of a theorem of Carlet, Dubrovin and Zhang regarding the relationship between the Toda lattice hierarchy and the NLS hierarchy. As an application, we give an improvement of an algorithm of computing correlators in hermitian matrix models.

GUE via Frobenius Manifolds. I. From Matrix Gravity to Topological Gravity and Back

“…leading to a second proof of the theorem (cf. [11,42]) via space/time duality (in genus zero: the Legendre-type transformation [18] of Dubrovin). This Frobenius manifold is often called an NLS Frobenius manifold [11,12,18], and will be discussed in details in the next of the article-series.…”