An improved method for Darboux transformation for the coupled inhomogeneous nonlinear Schrödinger system from plasma physics and nonlinear optics

► An improved method for Darboux transformation for the coupled inhomogeneous NLS system is presented. ► The Nth-iterated DT and the Nth-iterated Γ-R BT of the system are provided. ► The analytic one-/two-soliton-like solutions are obtained. ► The influences of the inhomogeneous parameters are discussed graphically.