External Perturbation Induced Soliton Dynamics with Self-frequency Shift in Cubic-Quintic Nonlinear Media

A soliton is a self-reinforcing, localized and particlelike wave-packet usually generated in a nonlinear medium and propagates with constant shape and velocity. In this work, soliton behavior is analyzed considering the real-world damping effect (δ) and its compensation in a cubic (b<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf>) -quintic (b<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf>) nonlinear medium considering perturbation term self frequency shift (SFS) (b<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</inf>), and nonlinear damping order controller (m). Using the Finite Element method, the effects of these physical terms were analyzed and we found that the dispersion and cubic nonlinearity can balance each other. The SFS causes disintegration and CQ nonlinearity may balance this effect. Moreover, with the increase in damping, pumping has to be increased to balance the losses. The range of normalized values of parameters were determined for stable soliton propagation and the initial value was found using relaxation method along with iterative approximations. Finally, the parameters b<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> = 0.2,b<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf>= 0.3,b<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> = 0.5,b<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</inf> = 0.05,δ= -0.04 were found from our investigation to observe the stable soliton. This study aims to investigate the soliton solutions using a unified method in a complex nonlinear media considering different extrinsic perturbations.