Transmission Characteristics Of Dark Solitons On Parabolic Background In Inhomogeneous Nonlinear Waveguide

The nonlinear Schrodinger equation about the transmission theoretical model of soliton in the medium and the common numerical method of solving nonlinear Schrodinger equation by substep Fourier method are briefly introduced on the basis understanding of soliton. General theoretical model of solitons in Kerr nonlinear response and the exact light and dark solutions of (1+1)-dimensional soliton under Kerr nonlinear response are described in detail. The transmission characteristics of dark solitons on the parabolic background in the non-uniform nonlinear waveguide are highlighted. We made the (2+1)-dimensional nonlinear Schrodinger equation as basis, made the light transport equation of non-uniform Kerr medium in the body as a model, and normalized by the appropriate transformation, transformed the light transport equation with the physical meaning into the constant coefficient nonlinear Schrodinger equation, then studied the self-similar evolution behavior of the parabolic light beam and the dark soliton stripe on the parabolic background. The results show that:parabolic light beam and dark soliton after cross the nonlinear potential barrier (potential well) self-similarly can still transport steadily, just the high order dark soliton will be split into a pair of gray soliton stripes during the evolution; In addition, we examined coexistence of some dark solitons, results show that in the case of other dark solitons interaction, it can still cross the potential barrier (potential well) self-similarly and transmit stably.