Dynamics of two-soliton molecule with impurities - Mohd Busul Aklan, Nor Amirah; Muhammad Husairi, Nur Fatin Ikhwani; Samiun, Anis Sulaikha; Umarov, Bakhram A. (Malaysian Mathematical Science Society (PERSAMA), 2023)
A soliton is the result of a delicate balance between dispersion-induced pulse self-broadening and nonlinearity-induced pulse self-narrowing, which brings in a constant propagation of the wave form and velocity. Additionally, soliton molecules are stable bound states that develop from two anti-phase bright solitons in a dipolar Bose-Einstein condensate, which represents another significant advance in the field. The behaviour of the two-soliton molecule of the nonlinear Schrödinger equation (NLSE) in the context of delta potential has been studied in this paper. Interaction of the solitons with the external potential will affect not only the speed, as classical particles do, but also the soliton’s properties and its physical locations. This work seeks to resolve the non-integrable perturbed NLSE of the two-soliton molecule analytically using the variational approximation method (VAM). VAM gives dynamical equations for the parameters of the soliton in the form of ordinary differential equations, and it only creates approximation results. The accuracy of the results is checked numerically by direct numerical simulation. The split-step approach and Fast Fourier Transform are two coding techniques used in the direct numerical simulation method to assist in issue solving. The results indicated that, the two-soliton molecule may be reflected, transmitted through, or trapped within the external potential depending on the different potential strength.