Bäcklund transformations, soliton solutions and wave functions of Kaup–Newell and Wadati–Konno–Ichikawa systems

Abstract

Using the Bargmann–Darboux method, the Bäcklund transformations, n-soliton solutions and corresponding wave functions of the Kaup–Newell and Wadati–Konno–Ichikawa systems are obtained. These results culminate in an algebraic recursive procedure for the determination of multisoliton solutions and their wave functions of the derivative and mixed derivative nonlinear Schrödinger equations iQt+Qxx∓iα(‖Q‖2Q)x ±β‖Q‖2Q=0, α>0, β≥0.