Quantum integrable Toda like systems

KP and Toda tau functions in Bethe ansatz

Recent work of Foda and his group on a connection between classical integrable hierarchies (the KP and 2D Toda hierarchies) and some quantum integrable systems (the 6-vertex model with DWBC, the finite XXZ chain of spin 1/2, the phase model on a finite chain, etc.) is reviewed. Some additional information on this issue is also presented.

Nonabelian Integrable Systems, Quasideterminants, and Marchenko Lemma

We find explicit (multisoliton) solutions for nonabelian integrable systems such as periodic Toda field equations, Langmuir equations, and Schrodinger equations for functions with values in any associative algebra. The solution for nonabelian Toda field equations for root systems of types A, B, C was expressed by the authors in a previous paper (q-alg/9701008) using quasideterminants introduced by the last two authors. To find multisoliton solutions of periodic Toda equations and other nonabelian systems we use a combination of these ideas with important lemmas which are due to Marchenko.

A型与C型q形变开Toda链的Lax矩阵与Cluster

Lax Matrices & Clusters for Type A & C Q-Deformed Open Toda Chain

本文研究q形变开Toda链的量子可积系统，证明由Coxeter字对参数化的量子Toda链族是单个cluster可积系统在不同cluster下的形式，且其正表示下的系统酉等价。

Integrable structure of melting crystal model with two q-parameters

This paper explores integrable structures of a generalized melting crystal model that has two $q$-parameters $q_1,q_2$. This model, like the ordinary one with a single $q$-parameter, is formulated as a model of random plane partitions (or, equivalently, random 3D Young diagrams). The Boltzmann weight contains an infinite number of external potentials that depend on the shape of the diagonal slice of plane partitions. The partition function is thereby a function of an infinite number of coupling constants $t_1,t_2,...$ and an extra one $Q$. There is a compact expression of this partition functi…

二维Toda可积层级的一种$(q,t)$形变

A $(q,t)$-deformation of the 2d Toda integrable hierarchy

本研究通过将对称代数提升为量子环面$\u27e8gl(1)$代数，构造出二维Toda可积层级的$(q,t)$形变，推导其双线性结构与多tau函数方程，定义普适细化tau函数并得到类$RLL$的二次方程，丰富了可积系统的形变理论。