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.
2013. , 34 p.