Abstract
Transient soliton dynamics for perturbatively driven and damped sG andφ4 solitons was found fort ≤Γ−1. The perturbed solitons remain stable with relativistic reduced time-dependent width. Internal oscillation modes of the solitons are asymptotically damped fort ≫Γ−1. There appears a relaxation regime with the field dependent superexponential relaxation of the soliton width which becomes exponential in the asymptotic regime.
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