Abstract
We present a family of self-accelerating stable pulses propagating in optical fiber and connecting a slowly-modulated quasi-cw background to an unstable zero level. Such solutions represent a generalization of the self-accelerating Airy beams observed in the linear regime to a nonlinear dissipative system modeled by a standard complex cubic Ginzburg-Landau equation corresponding to linear gain and a (fast) saturable absorber. They can also be viewed as a generalization of the well-studied problem of pulled fronts to include acceleration.
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