The cubic-quintic nonlinear schrödinger equation soliton scattering on the linear potentials - Aklana, Nor Amirah Busul; Umarov, Bakhram (2015)
One of the universal mathematical models, the Cubic-Quintic Nonlinear Schrödinger Equation (CQNLSE) describes many interesting problems in physics. It arises in 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 CQNLSE on the localized external potential has been studied. 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 was checked by direct numerical simulations of CQNLSE with soliton initially located far from potential. It was shown, in case of the potential in the form of delta function, 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.