Soliton scattering on the external potential in weakly nonlocal nonlinear media

The Nonlinear Schrödinger Equation (NLSE) is one of the universal mathematical models and it arises in a such diverse areas as plasma physics, condensed matter physics, Bose - Einstein condensates, nonlinear optics, etc. In this work the scattering of the soliton of the generalized NLSE on the localized external potential has been studied, taking into account the weak nonlocality of the media. We have applied the approximate analytical method, namely the variational method to derive the equations for soliton parameters evolution during the scattering process. The validity of approximations were checked by direct numerical simulations with soliton initially located far from potential. It was shown that depending on initial velocity of the soliton, the soliton may be reflected by potential or transmitted through it. The critical values of the velocity separating these two scenarios have been identified