Interaction Mechanism of the Parametrically Excited Solitons

The parametrically excited solitons manifest themselves with many distinct particle-like behaviors. Here the internal dynamics of the soliton-soliton interactions is explored both analytically and numerically. The results confirm the attraction between polarity-like solitons and the repulsion between opposite polarity ones. The attraction can make a pair of like polarity solitons form a standing (or oscillating) bound state. Therefore, multisolitons in an unbounded waveguide would asymptotically develop into an array of mutually independent standing soliton(s) or/and the bound state(s). It is shown that the bound state has two unidirectional momenta flowing toward the symmetric center, and thus the solitons do not perform the collisions in the classical sense. It is further demonstrated that the observed periodic “collisions” are actually due to the dissipative-induced collapses and the parametric recreations of solitons.