Interaction of solitons with delta potential in the Cubic-Quintic Nonlinear Schrodinger Equation

The study of soliton scattering of the Nonlinear Schrodinger 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. This paper concentrates on the effect of potentials to the soliton scattering in the generalized NLSE, Cubic-Quintic Nonlinear Schrodinger Equation (CQNLSE). To derive the equations for soliton parameters evolution during the scattering process, we have applied the approximate analytical method, namely the variational approximation method. The accuracy of approximations was checked by direct numerical simulations of CQNLSE with soliton initially located far from potential. In case of the potential in the form of delta function, depending on initial velocity of the soliton, it was shown the soliton may be reflected by potential or transmitted through it. The critical values of the velocity separating these two scenarios have been identified.