Preprint A509/2007
Global well-posedness and non-linear stability of periodic travelling waves solutions for a SchrÃ¶dinger-Benjamin-Ono system

Didier Pilod | Angulo, Jaime | Matheus, Carlos

**Keywords: **

The objective of this paper is two-fold: firstly, we develop a local and global (in time) well-posedness theory of 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 \emph{low-regularity} initial data in both periodic and continuous cases; secondly, a family of new periodic travelling 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 of the Jacobian elliptic function called {\it dnoidal}, and, moreover, we prove that all these periodic travelling waves are nonlinearly stable by perturbations with the same wavelength.