Exact spatial soliton solutions of the two-dimensional generalized nonlinear Schrödinger equation with distributed coefficients

Abstract

An improved homogeneous balance principle and an $F$-expansion technique are used to construct exact periodic wave solutions to the generalized two-dimensional nonlinear Schr\"odinger equation with distributed dispersion, nonlinearity, and gain coefficients. 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 establish a simple procedure to select different classes of solutions, using the dispersion and the gain coefficient in one case, or the chirp function and the gain coefficient in the other case, as independent parameter functions. We present a few characteristic examples of periodic wave and soliton solutions with physical relevance.