Time-localized dark modes generated by zero-wave-number-gain modulational instability

We report the emergence of a previously unexplored species of solitary waves, viz., time-localized dark modes in integrable and nonintegrable variants of the massive Thirring model and in the three-wave resonant-interaction system, which are models broadly used in plasma physics, nonlinear optics, and hydrodynamics. They are also interesting as basic models for the propagation of nonlinear waves in media without intrinsic dispersion. An essential finding is that the condition for the existence of time-localized dark modes in these systems, which develop density dips in the course of their evolution, coincides with the condition for the occurrence of the zero-wave-number-gain (ZWG) modulational instability (MI). Systematic simulations reveal that, whenever the ZWG MI is present, such dark modes are generically excited from a chaotic background as patches embedded in complex patterns.