Global Well-Posedness and Non-linear Stability of Periodic Traveling Waves for a Schrodinger-Benjamin-Ono System

Simple item page
dc.creatorAngulo, Jaime
dc.creatorMatheus, Carlos
dc.creatorPilod, Didier
dc.date2007-01-26
dc.date2007-08-01
dc.date.accessioned2026-07-07T08:21:35Z
dc.date.available2026-07-07T08:21:35Z
dc.descriptionThe 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 \emph{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 {\it dnoidal}, and, moreover, we prove that all these periodic traveling waves are nonlinearly stable by perturbations with the same wavelength.
dc.description38 pages; typos corrected and global well-posedness theorem (in the continuous case) reworked to follow closely the arguments of Colliander, Holmes and Tzirakis
dc.identifierhttps://arxiv.org/abs/math/0701786
dc.identifierhttp://arxiv.org/abs/math/0701786
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/135368
dc.subjectAnalysis of PDEs
dc.titleGlobal Well-Posedness and Non-linear Stability of Periodic Traveling Waves for a Schrodinger-Benjamin-Ono System
dc.typetext

Files

Collections

arXiv