Dynamics of gap solitons

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Abstract
It has been recently shown that in a nonlinear periodic medium there exist localized solutions of the stationary-wave equation called gap solitons (GS’s). Those GS’s are actually topological solitons (motionless in the laboratory frame). We present here a numerical study of the dynamical behavior of the gap solitons. We show that, in an infinite medium, the GS’s are generically unstable, giving rise to propagative solitary waves. In a semi-infinite medium, and above a precise value of the incident flux, we observe the generation of intermittent pulses propagating with a velocity close to c/2. Finally, we show that a true (motionless) GS can be physically produced by illuminating the system from both sides with equal-amplitude fluxes.