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| Dark solitons are intensity dips on a constant background with a phase jump across their intensity minimum. In physically relevant settings, linear/nonlinear dissipative effects are naturally important, and usually lead to the decay of the background; this way, the composite object composed by the background and the soliton is destroyed. In this context, a particularly interesting problem concerns the stabilization of dark solitons. Unlike their bright counterparts, i.e., solitons that decay at infinity, dark solitons -under the influence of perturbations- develop a shelf that propagates with speed determined by the background intensity. Using a newly developed perturbation theory we show that the perturbing effects give rise to a shelf that accompanies the soliton in its propagation. Although, the stable solitons are not affected by the shelf it remains an integral part of the dynamics otherwise missed so far in the literature. Furthermore, it is found that for certain values of the parameters a stable evolution can exist for both the soliton and the relative continuous wave background. |
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