Abstract
We introduce the phenomenon known as forced snaking to the study of gap solitons and use this notion to identify two distinct bifurcation diagrams organizing such solitons in the semi-infinite gap of the continuous cubic-quintic Gross-Pitaevskii equation with a spatially periodic potential. Standard snaking is found for small interpotential or lattice spacing while foliated snaking is present for large spacing. In each case, we determine the stability of the symmetric onsite and off-site solitons and show that multisoliton solutions of both types are stabilized when the spacing is sufficiently large, effectively quenching the interaction between the solitons. Finally, we show that the solitons unbind from the potential when subjected to sufficiently large asymmetric or symmetric perturbations and use direct numerical simulation to investigate their breakup and associated radiative losses as they propagate. A strongly nonlinear theory that captures key aspects of the depinning dynamics is provided.
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