Elastic and Inelastic Scattering of Flat-Top Solitons

We investigate the interaction between two flat-top solitons within the cubic-quintic nonlinear Schr\"odinger equation framework. Our study results point towards a significant departure of flat-top solitons collisional characteristics from the conventional behaviors exhibited in the scattering dynamics of two bright solitons. Our investigation outlines specific regimes corresponding to the dual flat-top solitons' elastic and inelastic collisions. We determine regimes in the parameter space where exchange in the widths of the interacting flat-top solitons is possible, even within the elastic collision domain. We find a periodic occurrence of completely elastic scattering of flat-top solitons in terms of the solitons' parameters. Investigating the internal energy transfers between the solitons and the emitted radiation reveals the origin of inelasticity in flat-top solitons collisions. We perform a variational calculation that accounts for the amount of radiation produced by the collision and hence provides further insight on the physics underlying the loss of elasticity of collisions.
Comment: 21 pages, 19 figures