Triple Wronskian vector solitons and rogue waves for the coupled nonlinear Schrödinger equations in the inhomogeneous plasma

The coupled inhomogeneous nonlinear Schrödinger (NLS) equations, which describe the propagation of two nonlinear waves in the inhomogeneous plasma, are investigated. By virtue of the triple Wronskian identities, the coupled inhomogeneous NLS equations are proved to possess the triple Wronskian vector solutions based on the non-isospectral Ablowitz-Kaup-Newell-Segur system. Solving the zero potential Lax pair, we give the bright N-soliton solutions from the triple Wronskian solutions. Amplitude and velocity of the soliton are related to the damping in the plasma. Overtaking interaction, head-on interaction and bound state of the two solitons are given. Solving the non-zero potential Lax pair, we construct the multi-parametric vector rogue-wave solutions of the coupled inhomogeneous NLS equations with the Darboux transformation. Influence of the linear and parabolic density profiles on the background density and amplitude of the rogue wave, is discussed. Bright-dark solitons together with a rogue wave are presented.