Quantum Potential Perturbed Soliton Dynamics with Self-steepening and Self-frequency Shift in Cubic-Quintic Nonlinear Media

A soliton is a localized and self-sustaining wave generally generated in a nonlinear medium that can propagate without considerable change in its shape. Solitons have applications in communication, medical imaging, astrophysics, and fluid dynamics. In this work, we analyze the soliton behavior in a cubic ($b_{2}$)-quintic ($b_{3}$) nonlinear medium considering perturbation terms: quantum (Bohm) potential (b), self-frequency shift (SFS) $\left(b_{5}\right)$ and self-steepening (SS) $\left(b_{4}\right)$. Using the Finite Element method, the effects of these perturbation terms on the stability of the soliton pulse have been thoroughly investigated. The parametric variation and a range of normalized values for different parameters for stable soliton propagation were determined. To find out the initial values relaxation method and curve fitting techniques along with iterative approximations are used. We found that the dispersion and cubic nonlinearity can balance the self-frequency shift. Moreover, with the increase in self-steepening, the soliton tends to become deformed and there is a small variation in the soliton shape with quantum potential if other parameters are wisely chosen. Finally, the parameters $b_{1}=0.15, b_{2}=0.6, b_{3}=$ 0.5, and $b_{4}=0.1$ were found from our investigation to observe the stable soliton. This study is important as it utilizes the finite element method of solution to demonstrate the possibility of finding solutions easily considering different physical phenomena in the same medium.