标题： 作为约束(2+1)-维可积系统的两矩阵弦模型 显示英文标题

标题： Two-Matrix String Model as Constrained (2+1)-Dimensional Integrable System

摘要： 我们证明了2-矩阵弦模型对应于一个耦合的系统，该系统由受特定“对称性”约束的$2+1$维KP方程和修正KP（$\KPm$）可积方程组成。后者的结合以及$\KPm$的Miura-Konopelchenko映射是矩阵弦方程的连续形式。$\KPm$的Miura变换和Bäcklund变换是潜在晶格结构的自然结果。受约束的$\KPm$系统等价于与分级${\bf SL(3,1)}$相关的$1+1$维广义KP-KdV层次结构。 我们用自由电流显式表示了这个层次结构，包括第二哈密顿结构的关联${\bf W(2,1)}$-代数。 显示英文摘要

摘要： We show that the 2-matrix string model corresponds to a coupled system of $2+1$-dimensional KP and modified KP ($\KPm$) integrable equations subject to a specific ``symmetry'' constraint. The latter together with the Miura-Konopelchenko map for $\KPm$ are the continuum incarnation of the matrix string equation. The $\KPm$ Miura and B\"{a}cklund transformations are natural consequences of the underlying lattice structure. The constrained $\KPm$ system is equivalent to a $1+1$-dimensional generalized KP-KdV hierarchy related to graded ${\bf SL(3,1)}$. We provide an explicit representation of this hierarchy, including the associated ${\bf W(2,1)}$-algebra of the second Hamiltonian structure, in terms of free currents.