Soliton solutions and a Bäcklund transformation for a generalized nonlinear Schrödinger equation with variable coefficients from optical fiber communications

Under investigation in this paper is a generalized nonlinear Schrödinger model with variable dispersion, nonlinearity and gain/loss, which could describe the propagation of optical pulse in inhomogeneous fiber systems. By employing the Hirota method, one- and two-soliton solutions are obtained with the aid of symbolic computation. Furthermore, a general formula which denotes multi-soliton solutions is given. Some main properties of the solutions are discussed simultaneously. As one important property of nonlinear evolution equation, the Bäcklund transformation in bilinear form is also constructed, which is helpful on future research and as far as we know is firstly proposed in this paper.