We present a method for solving integrable systems of nonlinear partial differential equations, known as the derivative nonlinear Schrodinger II system (DNSL II system), also called the Chen-Lee-Liu system. This is done by presenting a solution technique for the inverse scattering problem for the corresponding linear system of ordinary differential equations with energy-dependent potentials. The relevant inverse scattering problem is solved by establishing a system of linear integral equations, which we refer to as the Marchenko system of linear integral equations. In solving the inverse scattering problem we use the input data set consisting of a transmission coefficient, a reflection coefficient, and the bound-state information presented in the form of a pair of matrix triplets. Using our data set as input to the Marchenko system, we recover the potentials from the solution to the Marchenko system. By using the time-evolved input data set, we recover the time-evolved potentials, where those potentials form a solution to the integrable DNLS II system. For more information and the latex file, see https://ejde.math.txstate.edu/Volumes/2025/97/abstr.html
Mehmet Ünlü (Tue,) studied this question.