High-Order Solutions and Generalized Darboux Transformations of Derivative Nonlinear Schrodinger Equations

By means of certain limit technique, two kinds of generalized Darboux transformations are constructed for the derivative nonlinear Schrodinger equations (DNLS). These transformations are shown to lead to two solution formulas for DNLS in terms of determinants. As applications, several different types of high-order solutions are calculated for this equation.