标题： 关于利用开Toda链构造Davey-Stewartson I方程的解的研究 显示英文标题

标题： On the construction of solutions of the Davey--Stewartson I equation using an open Toda chain

摘要： 讨论了一种基于使用 dressing 链的有效方法来构造 Davey-Stewartson 型可积方程的显式解。该方法的应用以方程 DS I 为例，为此构造了一类新的显式解，其中包含两个任意函数的自由度。在这种情况下，作为 dressing 链使用了对应于简单李代数$A_2$的广义 Toda 格子。 显示英文摘要

摘要： An effective method for constructing explicit solutions to the Davey--Stewartson type integrable equations is discussed based on the use of a dressing chain. The application of the method is exemplified by the equation DS I, for which a new class of explicit solutions is constructed, containing freedom in two arbitrary functions. In this case the generalized Toda lattice corresponding to the simple Lie algebra $A_2$ is used as a dressing chain.