Abstract
The main concern of this paper is to investigate the Hirota equation with variable coefficients that can describe the pulse propagation in inhomogeneous fibers more realistically than its constant coefficients counterparts. A variety of complex wave solutions including new exact solutions, bright and dark soliton solutions, and similarity solutions are retrieved through $$G'/G$$ -expansion method with the aid of symbolic computation. The dynamical behaviors of the obtained solutions are illustrated using 3D- and corresponding contour plots in a graded-index waveguide.
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