New rogue waves and dark-bright soliton solutions for a coupled nonlinear Schrödinger equation with variable coefficients

In this paper, we construct explicit rogue wave solutions and dark-bright solutions for the inhomogeneous coupled nonlinear Schrödinger equation with variable coefficients by means of similarity transformations. Some explicit solutions to the coupled nonlinear Schrödinger equation with potentials and nonlinearities depending on both time and spatial coordinates are considered. We present the general approach and use it to calculate rogue wave solutions and dark-bright solutions for nonlinearities and potentials of physical interest in applications to Bose–Einstein condensates and nonlinear optics.