Boomeron- and Trappon Solitons InvestigatedAnalytically and Numerically

Abstract: This report presents an analysis of the phenomena of boomeron- and trappon solitons both analytically and numerically. These solitons are investigated in the (1+1) dimension, i.e. one spatial dimension plus the temporal dimension. The investigation regards the Boomeron equation (BE) and the non-linear Schrödinger equation (NLSE). Additional equations giving rise to these phenomena are also presented. A special focus of the investigation is the relation between the changing velocity and the polarization for the BE and the NLSE. For the NLSE, this is enabled through an interpretation of the components for the single-soliton solution. The BE is solved analytically through the inverse scattering transform. The analytical solutions for the BE and NLSE are compared with numerically obtained single-soliton solutions for the two equations respectively. The numerical solutions are conducted using a finite difference method (FDM) based on central difference.