Dabourx Transformation For Two Discrete Soliton Equations

In this paper, we have studied two discrete soliton equations, those are the so-called Belov-Chaltikian lattice and the well-known Generalized Toda lattice. We firstly in-troduce the discovery and development of the soliton theory, along with some classical methods those have been used to obtain explicit solutions of soliton equations; Then we construct the Darboux transfromation of the Belov-Chaltikian lattice, prove our results completely in terms of the theory, obtain the new solutions of that equation and some figures are plotted; After that we construct the Darboux transfromation of the General-ized Toda lattice, prove our results in detail, obtain the new solutions of the generalized Toda lattice, and some figures are plotted.