Darboux transformations, infinitesimal symmetries and conservation laws for the nonlocal two-dimensional Toda lattice

摘要

The technique of Darboux transformation is applied to the nonlocal partner of the two-dimensional periodic A(n-1) Toda lattice. This system is shown to admit a representation as the compatibility conditions of direct and dual overdetermined linear systems with a quantized spectral parameter. We give the generalization of the Darboux transformation technique on linear equations of this type. We present the connections between the solutions of overdetermined linear systems and their expansions in series in the neighbourhood of singular points. The solutions of the nonlocal Toda lattice and infinite hierarchies of the infinitesimal symmetries and conservation laws are obtained. [References: 32]