Multi-peak soliton dynamics and decoherence via the attenuation effects and trapping potential based on a fractional nonlinear Schrödinger cubic quintic equation in an optical fiber

Fiber optic research continues to develop due to the need for fast information technology. The input signal in an optical fiber is in the form of a soliton wave that propagates in the fiber with a balanced index of refraction, dispersion, and diffraction. Fiber optics may lose some of the signal over time if they solely use a nonlinear refractive index. This study aims to examine into the dynamics and decoherence of multi-peak solitons caused by electromagnetic signal attenuation and potential trap in the propagation via optical fibers. The methods used start with the stationary solution of the nonlinear Schrödinger Cubic Quintic equation, the Newton-Raphson method, and the fourth-order Runge-Kutta. In stationary solutions, the p (state energy) and ρ (Lèvy index) values affect the number, pulse width, and height of soliton peaks. Increased p and ρ values lead to increased instability, causing the data transmitted into the optical fiber to collapse and become unreadable by the receiver. In the excited state (p > 0), the decoherence phenomenon occurs and causes wave instability and destruction. In term of energy intensity, a stable form of transmission in the ground state has a pattern of continuously weakening, decreasing, and smoothing, while in the excited state there is a spike in the intensity of the electromagnetic wave. Based on this study, multi-peak solitons can only be applied for propagation distances, which tend to be short due to their dynamics and decoherence.