title: Spontaneous breaking of the spatial homogeneity symmetry in wave turbulence.
abstract: We report a surprising new result for wave turbulence which may have broader ramifications for general turbulence theories. Spatial homogeneity, the symmetry property that all statistical moments are functions only of the relative geometry of any configuration of points, can be spontaneously broken by the instability of the finite flux Kolmogorov-Zakharov spectrum in certain (usually one dimensional) situations. As a result, the nature of the statistical attractor changes dramatically, from a sea of resonantly interacting dispersive waves to an ensemble of coherent radiating pulses.
authors.affiliation: Department of Mathematics, The University of Arizona, Tucson, Arizona 85721-0089, USA.
authors.forename: Alan C
authors.initials: AC
authors.lastname: Newell
authors.forename: Benno
authors.initials: B
authors.lastname: Rumpf
authors.forename: Vladimir E
authors.initials: VE
authors.lastname: Zakharov