Analytical soliton solutions for the general nonlinear Schrödinger equation including linear and nonlinear gain (loss) with varying coefficients

An improved homogeneous balance principle and an F-expansion technique are used to construct analytical solutions to the generalized nonlinear Schrödinger equation with distributed coefficients and linear and nonlinear gain (or loss). For limiting parameters, these periodic wave solutions acquire the form of localized spatial solitons. Such solutions exist under certain conditions, and impose constraints on the functions describing dispersion, nonlinearity, and gain (or loss). We present a few characteristic examples of periodic wave and soliton solutions with physical relevance.