Abstract
We investigate the mobility of discrete cavity solitons in arrays of coupled quadratic nonlinear resonators driven by an inclined holding beam. Unlike in transversely homogeneous cavities the inherent discreteness hinders or even prevents the soliton motion. As a consequence for the same system parameters one type of soliton may still be at rest, whereas others already move. This feature gives rise to collisions between these different types. To study the soliton dynamics in more detail we take advantage of a perturbation theory and derive soliton velocities semianalytically.
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