标题： Toda型三维格子的对称性 显示英文标题

标题： Symmetries of Toda type 3D lattices

摘要： Davey-Stewartson类型耦合系统的一类与二维Toda类型格子的一类之间的对偶性被讨论。 对于最近发现的可积格子，其对称性层次被描述。 给出了二阶和三阶对称性的显式形式。 给出了相应的耦合系统。 提出了一种构造耦合系统精确解的原始方法，该方法基于dress链的Darboux可积约化。 作为示例，给出了一些与Volterra格子相关的耦合系统的新的解。 显示英文摘要

摘要： The duality between a class of the Davey-Stewartson type coupled systems and a class of two-dimensional Toda type lattices is discussed. For the recently found integrable lattice the hierarchy of symmetries is described. Second and third order symmetries are presented in explicit form. Corresponding coupled systems are given. An original method for constructing exact solutions to coupled systems is suggested based on the Darboux integrable reductions of the dressing chains. Some new solutions for coupled systems related to the Volterra lattice are presented as illustrative examples.