Global Well-Posedness and Non-linear Stability of Periodic Traveling Waves for a Schrödinger-Benjamin-Ono System
نویسندگان
چکیده
The objective of this paper is two-fold: firstly, we develop a local and global (in time) wellposedness 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 lowregularity 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.
منابع مشابه
Global Well-Posedness and Non-linear Stability of Periodic Travelling Waves Solutions for a Schrödinger-Benjamin-Ono System
The objective of this paper is two-fold: firstly, we develop a local and global (in time) wellposedness theory of 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 lowregularity initial data in both periodic and continuous cases; secondly, a family of new periodic travelling wa...
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