Exploring optical solitons, modulation instability and chaotic behavior in the Schrödinger-Hirota equation - Demirbilek, Ulviye; Danladi, Ali; Bulut, Hasan; Seadawy, Aly R.; Ahmed, Karim K. (Springer-Verlag Italia Srl, 2025)
Optical soliton solutions for nonlinear composite models are of great importance in the area of nonlinear optics and optical communication systems. This study focuses on the nonlinear Schr & ouml;dinger-Hirota equation that regulates the diffusion of optical solitons under the influence of both dispersion and nonlinear effects. The aim is to derive different forms of soliton solutions, examine their stability, and analyze the dynamics of the system under fault effects. To achieve this, we used an efficient and reliable analytical approach known as the improved modified Sardar-sub equation method. This method derives several optical soliton solutions, such as dark, singular, and periodic solitons. Each solution was validated by returning to the original nonlinear Schr & ouml;dinger-Hirota equation with the help of software. Furthermore, analysis of modulation instability was performed by linearization of the disturbed model and derivation of the gain spectrum. The proposed method successfully revealed a rich set of solutions for the target model. These solutions were validated under certain parametric limitations. Graphical representations, including 3D plots, contour, and 2D plots, were created to visualize their physical behavior for the selected solutions. A gain spectrum of modulation instability was presented to determine the conditions under which stable wave propagation occurs. Additionally, the system's bifurcation structure, chaotic dynamics, and sensitivity analysis were examined and presented graphically. This work provides a comprehensive investigation of nonlinear reduced Hirota models from both analytical and dynamical perspectives. The obtained results are different from the other solutions available in the literature. The integration of improved modified Sardar-Sub equation method with symbolic validation and modulation instability analysis highlights the robustness and versatility of the approach. This study also contributes novel insights into the stability and chaotic transitions of higher-order nonlinear optical models, supporting their application to real-world optical systems and advanced fiber communication technologies.
Keywords: The nonlinear Schr & ouml;dinger-Hirota equation; Modulation instability; Bifurcation analysis; Sensitivity analysis; Chaos analysis