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### Open Access Journals

CPAA

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 Schrödinger-Benjamin-Ono system) for

*low-regularity*initial data in both periodic and continuous cases; secondly, a family of new periodic traveling waves for the Schrödinger-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.## Year of publication

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