Simulations for the Schrödinger–Hirota equation arising in nonlinear optics in the presence of chromatic dispersion

The main objective of this work is to study the accurate traveling wave behavior of the optical pulses described by the Schrödinger–Hirota equation taking into account the chromatic dispersion term. This study uses the extended-$\left(\frac{G^{\prime }}{G^2}\right)$ and the $exp(-\varphi \left(\varpi \right))$-expansion methods to get the exact closed form wave solutions to the Schrödinger–Hirota problem. Nonlinearity with Kerr rule is used to analyze the aforementioned model, leading to some novel conclusions. A variety of dynamical wave patterns have been observed through graphical simulations of the retrieved solutions. The reported results may be helpful in further explanation in optical fibers, communication systems and nonlinear optics.