DARBOUX TRANSFORMATIONS FOR A GENERALIZATION OF THE NONLINEAR SCHRO?DINGER EQUATION AND ITS REDUCTIONS

In this paper, we introduce a 2 x 2 matrix spectral problem with two potentials to derive a generalization of the nonlinear Schro center dot dinger system that can be reduced to four important integrable equations: a generalization of the nonlinear Schro center dot dinger equation, a combined nonlinear Schro center dot dinger and derivative nonlinear Sch-ro center dot dinger equation, and a combined nonlinear Schro center dot dinger and Chen-Lee-Liu equation, a combined nonlinear Schro center dot dinger and Gerdjikov-Ivanov equation. With the help of a gauge transformation between the corresponding Lax pairs, Darboux transformations for the generalization of the nonlinear Schro center dot dinger system and its reductions are con-structed, by which explicit solutions for the generalization of the nonlinear Schro center dot dinger system and its reduction can be engendered from their known solutions. As an appli-cation, we obtain various explicit solutions of the four integrable equations, including one-soliton, two-soliton, periodic solutions and others.