On the Dynamics of Soliton Waves in a Generalized Nonlinear Schrödinger Equation

The main objective of the present paper is to investigate the dynamics of soliton waves in a generalized nonlinear Schrödinger (GNLS) equation. To achieve such a goal, the real and imaginary portions of the GNLS equation are first extracted using a complex wave transformation. Solitons and Jacobi elliptic structures of the governing model, describing the propagation of femtosecond pulses in nonlinear optical fibers, are then constructed through applying the modified Jacobi elliptic expansion method (MJEEM). In the end, by employing a series of 2 and 3D-dimensional numerical representations, it is exposed that the width of bright and dark solitons respectively decreases and increases, while the amplitude of both waves decreases with the increase of nonlinear parameters.