Nonlinear ocean wave propagation in a fractional perturbed Gerdjikov–Ivanov model with higher-order dispersive effects

Nonlinear dispersive wave propagation governs complex physical phenomena in both nonlinear optics and hydrodynamics, including optical fiber communications, ultrafast photonic systems, coastal environments, and marine systems, where higher-order nonlinear interactions and dispersive effects significantly influence wave evolution. Mathematically, the perturbed Gerdjikov–Ivanov (GI) equation belongs to the derivative nonlinear Schrödinger hierarchy and serves as a canonical model for studying higher-order nonlinear dispersive systems; its mathematical structure, particularly the quintic nonlinearity and self-steepening terms, shares formal analogies with higher-order Dysthe-type models for nonlinear ocean surface waves in deep water, where similar balance mechanisms between nonlinearity and dispersion govern wave evolution. In this study, a perturbed fractional GI model incorporating quintic nonlinearity, self-steepening, Raman-type perturbation effects, and the conformable fractional derivative is investigated as a mathematical framework, with results interpreted in both optical and broader nonlinear dispersive wave contexts. Although related higher-order nonlinear wave models have been extensively studied, the combined influence of higher-order perturbation mechanisms and fractional-order effects on nonlinear ocean wave dynamics has received limited attention. By employing efficient analytical techniques, several families of exact solitary wave solutions are derived, including bright, dark, periodic, and localized nonlinear wave structures under both classical and conformable fractional formulations. The dynamical behavior of the obtained solutions is illustrated through two-dimensional and three-dimensional graphical visualizations, demonstrating the significant influence of the fractional-order parameter on wave amplitude, propagation speed, localization, and waveform evolution. The results reveal that fractional-order effects provide an effective mechanism for controlling nonlinear dispersive wave propagation, while higher-order perturbation terms modify the structural and interaction characteristics of solitary waves, as evidenced by the wave topology changes observed across solution families. These findings contribute to the theoretical understanding of nonlinear dispersive wave dynamics and provide analytical insights applicable to pulse compression, signal localization, and energy management in nonlinear fiber-optic and photonic crystal fiber systems. Applications to shallow-water and coastal hydrodynamic modeling remain prospective and would require further validation against ocean-wave experimental data and numerical stability analysis.