Traveling waves, chaos and solitons in a cubic-quintic nonlinear optical media

Abstract

In this paper, we theoretically investigate the bifurcations and exact traveling wave solutions of a weakly nonlinear Schr & ouml;dinger equation that includes higher-order dispersion effects. By analyzing the phase portraits, we predict the exact analytically solutions for the model equation. The predicted periodic waves and solitary waves of the model are determined using the Riccati sub-ODE and elliptic expansion methods, respectively. The proposed computational approaches in comparison to traditional computational techniques, offer powerful improvements in accuracy, efficiency, and the ability to identify a wide range of solitons solutions. Through linear stability analysis, we derive an analytical expression for the instability gain and analyze its main characteristics. Finally, we assess the robustness and stability of the solitary wave solutions through numerical simulations and compare the accuracy of the analytical and numerical results. The outcomes may be used as a guide for the production of solitons and ultra-short optical pulses for potential applications in the telecommunication domain.