Dynamics and soliton solutions of the perturbed Schrödinger-Hirota equation with cubic-quintic-septic nonlinearity in dispersive media

This study systematically investigates the dynamics of the perturbed Schrödinger-Hirota equation with cubic-quintic-septic nonlinearity under spatiotemporal dispersion, providing insights into soliton propagation in dispersive media. We begin by examining the system's phase portrait and chaotic behavior, followed by the derivation of exact traveling wave solutions, including optical solitons and periodic solutions, using an enhanced algebraic method. The findings are vividly illustrated through three-dimensional and two-dimensional graphical simulations, which analyze the impact of key parameters on the solutions. This study not only presents a variety of optical soliton solutions, but also clarifies the underlying dynamics, offering theoretical guidance for fiber optic communication systems and holding significant applied value for achieving more efficient and reliable optical communications.