title: Transition of weak wave turbulence to wave turbulence with intermittent collapses.
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.
authors.affiliation: Department of Mathematics, Southern Methodist University, Dallas, Texas 75275-0156, USA.
authors.forename: Benno
authors.initials: B
authors.lastname: Rumpf
authors.affiliation: Department of Mathematics, Southern Methodist University, Dallas, Texas 75275-0156, USA.
authors.forename: Thomas Y
authors.initials: TY
authors.lastname: Sheffield