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2009, Volume 8, Issue 3: 815-844. Doi: 10.3934/cpaa.2009.8.815
This issue Previous Article Exponential attractors for second order lattice dynamical systems Next Article Classical limit for linear and nonlinear quantum Fokker-Planck systems

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

  • 1.

    IME-USP, Department of Mathematics, Rua do Matão 1010, Cidade Universitária, CEP 05508-090, São Paulo, SP

  • 2.

    IMPA, Estrada Dona Castorina 110, CEP 22460-320 Rio de Janeiro, RJ

  • 3.

    UFRJ, Institute of Mathematics, Federal University of Rio de Janeiro, P.O. Box 68530, CEP: 21945-970, Rio de Janeiro, RJ

Received:  April 30, 2008
Revised:  September 30, 2008
Published:  April 2009
Abstract Related Papers Cited by
    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 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.
    Mathematics Subject Classification: Primary: 35Q55, 35Q51; Secondary: 76B25, 76B15.

    Citation:
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