Collision dynamics of a discrete soliton in uniform waveguide arrays

Abstract

We investigate the collision dynamics of a discrete soliton (DS) pair in a realistic semi-infinite nonlinear waveguide array (WA) in the context of diffractive resonant radiation (DifRR). Depending on the initial amplitude ( A 0 ) and wavenumber ( k 0 ), a co-moving pair of identical DSs either collide elastically or merge to form a discrete breather. For a large amplitude and small wavenumber, DSs do not interact to form a bound state. We map the domain of interaction by iterative simulation and present a phase plot in ( A 0 − k 0 ) parameter space. To grasp the collision dynamics, we develop an analytical treatment based on a variational method that leads us to a set of ordinary differential equations describing the collision mechanism. Our analytical results corroborate our numerical data. We further investigate the role of initial phase detuning between two identical DSs and observe a periodic energy exchange during their interaction. A varied degree of energy exchange occurs when two DSs with different wavenumbers collide, which results in three distinct output states accompanied by DifRR generation. Extending our investigation to a more generalized condition by taking a nonidentical DS pair, we find unique secondary radiation in -space that originates due to the interaction of DSs during collision. The nature of this collision mediated secondary radiation is found to be different from usual DifRR. Our results shed light on the interesting aspects of the collision dynamics of a DS pair in a nonlinear WA and are useful in understanding the complex mechanism.