Gaussian function on soliton scattering of generalized Nonlinear Schrödinger Equation: variational analysis - Mohd Busul Aklan, Nor Amirah; Ramli, Nor Nadira Amani; Umarov, Bakhram A. (IIUM Press, 2022)
In a nonlinear dispersive medium, a soliton is a large-amplitude pulse excitation that can propagate with constant form and velocity which maintains its original shape. The emergence of a soliton is the result of a delicate balance between dispersion-induced pulse self-broadening and nonlinearity-induced pulse self-narrowing. Critically, the realisation of this equilibrium depends on the form of nonlinearity. Solitons can be excited in a broad range of physical structures, including water waves, plasma, optical fibre, spin waves, deoxyribonucleic acid, and ultra-cold atoms. Previous research studies inspire us to study soliton more thoroughly by expanding the NLSE form to a more generalised version. This research also investigates the effect of the potential towards soliton alongside the propagation of the wave. Analytical and numerical methods are applied to solve the Cubic-Quintic Nonlinear Schrödinger Equation in order to achieve the objectives of this analysis. The Variational Approximation Method (VAM) is applied to calculate the soliton parameters equations during the scattering process once the soliton is originally far from the potential. Direct numerical simulations are used to verify the accuracy of the soliton approximation results from VAM. The findings revealed that relying on the soliton’s initial velocity and potential strength, the soliton can be transmitted through, damaged, or reflected by potentials.