标题： 关于非阿贝尔Toda$A_2^{(1)}$模型及相关层次结构 显示英文标题

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

摘要： 我们研究了两个已知的具有三维配置空间的可积手征型模型的极限情况。 初始模型之一是非阿贝尔Toda$A_2^{(1)}$模型，另一个是通过对称性方法由A.G. Meshkov和作者之一发现的。 通过构建其完整的积分集和通解，确立了约化模型的C-可积性。 这些模型的广义对称代数被描述为将积分映射到对称性的算子。 已知Liouville型系统的积分定义了其广义对称性的Miura型变换。 这一事实使我们找到了一些新的Yajima-Oikawa型系统。 我们提出了其中一个系统的递归算子。 显示英文摘要

摘要： 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.