Abstract
We consider the existence of a dynamically stable soliton in the one-dimensional cubic-quintic nonlinear Schrödinger model with strong cubic nonlinearity management for periodic and random modulations. We show that the predictions of the averaged cubic-quintic NLS equation and modified variational approach for the arrest of collapse coincide. The analytical results are confirmed by numerical simulations of one-dimensional cubic-quintic NLS equation with rapidly and strongly varying cubic nonlinearity coefficient.
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