Bifurcation and exact optical solutions in weakly nonlocal media with cubic-quintic nonlinearity

Abstract
In this study, we explore the bifurcation and optical soliton solutions in weakly nonlocal media with cubic-quintic nonlinearity, which are significant for understanding optical soliton propagation in nonlocal nonlinear systems. The cubic-quintic nonlinear Schrödinger equation, including weak nonlocality, is introduced to model the evolution of soliton trains in optical fibers under the influence of a nonlocal medium. Using a traveling wave transformation, the equation is reduced to a singular dynamical system and further transformed into a regular dynamical system through changing variables. The study confirms the equivalence of the first integrals for both systems and provides a detailed analysis of phase portraits, emphasizing their geometric and topological features. Additionally, the unified Riccati equation expansion method is applied to derive exact solutions, including periodic, dark, and singular soliton solutions. 2D and 3D graphical representations of the solutions are presented to illustrate their physical properties, with parameters chosen to highlight the effects of cubic-quintic nonlinearity and weak nonlocality. These findings offer insights into the dynamics of nonlinear wave propagation in optical systems and contribute to advancements in nonlocal nonlinear optics and soliton theory.

Author
Hajar Farhan Ismael

DOI
https://doi.org/10.1007/s11071-025-11305-x

Publisher

ISSN
1573-269X

Publish Date: