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Global well-posedness and non-linear stability of periodic traveling wavesfor a Schrödinger-Benjamin-Ono system

Authors
Type
Published Article
Journal
Communications on Pure & Applied Analysis
Publisher
American Institute of Mathematical Sciences (AIMS)
Publication Date
Jun 27, 2009
Volume
8
Issue
3
Pages
815–844
Identifiers
DOI: 10.3934/cpaa.2009.8.815
OAI: oai:www.producao.usp.br:BDPI/16692
Source
USPC - SET - SVS
Keywords
License
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External links

Abstract

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.

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