Interaction of solitons with external potentials in the Generalized Nonlinear Schrödinger Equations

Abstract

Soliton is referred as a solitary wave that propagates with unchanged shape and velocity in nonlinear dispersive media. It is caused by a cancellation of nonlinearity and dispersion effects in the medium. The study of soliton scattering of the Nonlinear Schrödinger Equation (NLSE) has brought a wide focus by researchers especially in physics field such as Bose-Einstein condensates, nonlinear optics, plasma physics, condensed matter physics, etc. Therefore, it motivates us to extend the NLSE form, and concentrate on the effect of potentials to the soliton scattering in the generalized NLSE. In order to achieve the objectives, we construct analytical and numerical studies of solitons interaction with potential barriers and wells within the Generalized Nonlinear Schrödinger Equations (GNLSE). Then, we identify the interaction of a single soliton and further, we investigate two-soliton molecule of the GNLSE on the localized external potentials. In addition, we analyze the soliton scattering of GNLSE in weak and strong nonlocal nonlinear media when come to the potentials. Lastly, we investigate numerically the role of bound states in the potential well on the result of scattering of soliton molecules. The variational approximation method was employed to derive the equation for soliton parameters evolution during the scattering process. The accuracy of approximations was checked by direct numerical simulations of CQNLSE with soliton initially located far from potential. The results shown that, by considering different form of the potentials, depending on initial velocity of the soliton, it was shown the soliton may be reflected by potential or transmitted through it. Also, the critical values of the velocity separating these two scenarios have been identified.