Abstract
We study the dynamics of one-dimensional nonlinear waves with a square-root dispersion. This dispersion allows strong interactions of distant modes in wave-number space, and it leads to a modulational instability of a carrier wave interacting with distant sidebands. Weak wave turbulence is found when the system is damped and weakly driven. A driving force that exceeds a critical strength leads to wave collapses coexisting with weak wave turbulence. We explain this transition behavior with the modulational instability of waves with the highest power: Below the threshold the instability is suppressed by the external long-wave damping force. Above the threshold the instability initiates wave collapses.
1 More- Received 10 June 2015
DOI:https://doi.org/10.1103/PhysRevE.92.022927
©2015 American Physical Society