中文摘要：

一新(2+1 ) 维的格子方程被介绍在联合 Toda 格子和相对论的 Toda 格子(TL-RTL ) 的层次在开始的二个成员之上基于方程在(1+1 ) 尺寸。为联合 TL-RTLequations 的层次的 Darboux 转变被构造。在联合 TL-RTLequations 的层次的开始的二个成员的答案，以及新(2+1 ) 维的格子方程被 theDarboux 明确地获得转变。

英文摘要：

A new （29-1）-dimensional lattice equation is presented based upon the first two members in the hierarchy of the combined Toda lattice and relativistic Toda lattice （TL-RTL） equations in （19991） dimensions. A Darboux transformation for the hierarchy of the combined TL-RTL equations is constructed. Solutions of the first two members in the hierarchy of the combined TL-RTL equations, as well as the new （29-1）-dimensional lattice equation are explicitly obtained by the Darboux transformation.