On non-Abelian Toda $A_2^{(1)}$ model and related hierarchies

TL;DR

This paper investigates limiting cases of integrable non-Abelian Toda models, establishing their C-integrability, describing their symmetry algebras, and deriving new related systems with recursion operators.

Contribution

It provides a detailed analysis of the non-Abelian Toda $A_2^{(1)}$ model, constructs complete integrals and solutions, and introduces new Yajima-Oikawa type systems with recursion operators.

Findings

C-integrability of reduced models is established.

Complete sets of integrals and solutions are constructed.

New Yajima-Oikawa type systems with recursion operators are found.

Abstract

We study limiting cases of the two known integrable chiral-type models with tree-dimensional configuration space. One of the initial models is the non-Abelian Toda $A_2^{(1)}$ model and the other was found by means of the symmetry approach by A.G. Meshkov and one of the authors. The C-integrability of the reduced models is established by constructing their complete sets of integrals and general solutions. A description of the generalized symmetry algebras of these models is given in terms of operators mapping integrals into symmetries. The integrals of the Liouville-type systems are known to define Miura-type transformations for their generalized symmetries. This fact allowed us to find a few new systems of the Yajima-Oikawa type. We present a recursion operator for one them.