Soliton solutions of coupled inhomogeneous nonlinear Schrödinger equation in plasma

We consider the coupled system of inhomogeneous damped nonlinear Schrödinger equation which explains wave propagation in plasma. We generalise the (2 × 2) Ablowitz, Kaup, Newell and Segur (AKNS) formalism and construct the linear eigenvalue problem of coupled system. We use the Bäcklund transformation method to derive explicit form of one-soliton solution.