Bright solitons on a continuous wave background for the inhomogeneous nonlinear Schrödinger equation in plasma

In this paper, the inhomogeneous damped nonlinear Schrödinger equation (NLS) which describes wave propagation in plasmas is investigated. Based on Husimi's transformation and lens-type transformation, we reduce the inhomogeneous NLS equation to the standard NLS equation and thus the bright soliton solutions on a continuous wave (cw) background are constructed and discussed. Besides, we also consider the inhomogeneous NLS equation with different damping coefficients. Based on the perturbation theory for bright solitons, the approximate bright soliton solutions for such an equation are obtained, which are in good agreements with direct numerical simulations.