A class of exact solutions of the generalized nonlinear Schrödinger equation

The generalized nonlinear Schrödinger equation, studied in this paper, is an important model of nonlinear excitations of matter waves in Bose—Einstein condensates. Through a natural transformation and the Hirota bilinear method, N bright and dark soliton solutions are obtained. Based on Jacobi theta functions, periodic-like solutions, which are periodic in x, are also presented.