Constrained KP Hierarchies: Darboux-B\"acklund Solutions and Additional Symmetries

TL;DR

This paper explores the interplay of non-isospectral symmetries and Darboux-Bäcklund transformations in constrained KP hierarchies, providing solutions for discrete multi-matrix string models using Wronskian tau-functions.

Contribution

It introduces the concept of additional non-isospectral symmetries in constrained KP hierarchies and applies them to solve discrete multi-matrix string models.

Findings

Demonstrates the role of non-isospectral symmetries in constrained KP hierarchies.

Provides explicit solutions for discrete multi-matrix string models.

Uses Wronskian tau-functions of graded SL(m,1) hierarchies.

Abstract

We illustrate the basic notions of {\em additional non-isospectral symmetries} and their interplay with the discrete {\em \DB transformations} of integrable systems at the instance of {\em constrained Kadomtsev-Petviashvili} (\cKP) integrable hierarchies. As a main application we present the solution of discrete multi-matrix string models in terms of Wronskian $\t$-functions of graded $SL(m,1)$ \cKP hierarchies.