GLOBAL WELL-POSEDNESS AND NON-LINEAR STABILITY OF PERIODIC TRAVELING WAVES FOR A SCHRODINGER-BENJAMIN-ONO SYSTEM

The objective of this paper is two-fold: firstly, we develop a local and global (in time) well-posedness theory for a system describing the motion of two fluids with different densities under capillary-gravity waves in a deep water flow (namely, a Schrodinger-Benjamin-Ono system) for low-regularity initial data in both periodic and continuous cases; secondly, a family of new periodic traveling waves for the Schrodinger-Benjamin-Ono system is given: by fixing a minimal period we obtain, via the implicit function theorem, a smooth branch of periodic solutions bifurcating a Jacobian elliptic function called dnoidal, and, moreover, we prove that all these periodic traveling waves are nonlinearly stable by perturbations with the same wavelength.

Taxonomic revision of Gripopteryx (Pictet, 1841) (Plecoptera: Gripopterygidae)

The genus Gripopteryx is revised and two new species are described, G. japi n. sp. from southeastern Brazil, and G. clemira n. sp. from northeastern Brazil. The male of G. brasiliensis Samal, 1921 and the female of G. flinti Froehlich, 1993 are described. New figures for G. maculosa Jewett, 1960, for the male of G. reticulata Brauer, 1866, and for the female of G. brasiliensis are provided. Keys to adult males and to nymphs are provided.