Unified solutions for three derivative nonlinear Schrödinger equations and reductions

Abstract In this paper, we construct unified solutions for three derivative nonlinear Schr"odinger systems using different variable transformations but the same double Wronskian form. Through reductions, we also derive unified solutions for three classical derivative nonlinear Schr"odinger equations and three nonlocal derivative nonlinear Schr"odinger equations, respectively. The unified solutions are provided without the need for gauge transformations, though the resulting solutions for the three equations are shown to be connected through gauge transformations. Taking the classical Gerdjikov-Ivanov equation and the nonlocal Gerdjikov-Ivanov equation as examples, we present the dynamics of soliton solutions.