Bright and dark solitons for the fifth-order nonlinear Schrödinger equation with variable coefficients

Abstract

In this work, a fifth-order nonlinear Schrödinger equation with variable coefficients is investigated, which represents the diffusion of ultrashort pulses in incompatible optical fibers. With the aid of two direct functions, some non-traveling wave bright and dark soliton solutions are obtained. Via the G′/G-expansion method, the non-traveling wave hyperbolic-type and trigonometric-type solutions are studied. Finally, we show the dynamic properties and characteristics of these derived results by using some three-dimensional figures and contour figures.