DT And Soliton Solutions Of The Couple Nonlinear Schr(?)dinger Equations

The soliton theory is an important branch of applied mathematics and mathematical physics, and an important part of the nonlinear science. It has important applications in fluid mechanics, nonlinear optics, classical and quantum fields theories etc. It is one of the most active fields in science. There are many methods to obtain explicit solutions of nonlinear partial differential equations in the soliton theory. Among the various approaches, the Darboux transformation is a very powerful tool, it can find explict solutions of soliton equations from a trivial seed.In this paper, we use the Darboux transformation for generating the explicit solutions of the four (1+1)-dimensional soliton equations and several interesting figures of the solitonian solutions are plotted.There are three sections in the paper. The first section is an introduction about the history of the soliton theory and the Darboux transformation.In the second section, we apply to the basic Darboux transformation's theory and consider the a Lax pairswherewhich correspond to the couple nonlinear Schr(o|¨)dinger equations...