title: Stability analysis of spatiotemporal cnoidal waves in cubic nonlinear media.
abstract: We analyze numerically the modulational instability of spatiotemporal cnoidal waves of cn, dn, and sn types that are periodic along a single space coordinate and are uniform in time. The band of possible increments is calculated for all three types of cnoidal waves as a function of parameter describing the degree of localization of the wave field energy. It is shown that this band transforms into a set of discrete values for waves of cn and dn types in the limit of strong spatial localization. Simulation of perturbed cnoidal-wave propagation revealed suppression of collapse and multiple-wave filamentation on the developed stage of instability. Different instability scenarios are considered in detail.
authors.affiliation: Physics Department, M. V. Lomonosov Moscow State University, 119899 Vorobiovy Gory, Moscow, Russia.
authors.forename: Victor A
authors.initials: VA
authors.lastname: Aleshkevich
authors.forename: Alexey A
authors.initials: AA
authors.lastname: Egorov
authors.forename: Yaroslav V
authors.initials: YV
authors.lastname: Kartashov
authors.forename: Victor A
authors.initials: VA
authors.lastname: Vysloukh
authors.forename: Anna S
authors.initials: AS
authors.lastname: Zelenina