On non-Abelian Toda A2 (1) model and related hierarchies

We study limiting cases of the two known integrable chiral-type models with three-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 Meshkov and Demskoi [Theor. Math. Phys. 134, 351 (2003)] . 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 operator 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.