Nonlinear stability, excitation and soliton solutions in electrified dispersive systems

M.F. El-Sayed

Mathematics and Computers in Simulation (MATCOM), 2008, vol. 79, issue 3, 242-257

Abstract: A weakly nonlinear theory of wave propagation in two superposed dielectric fluids in the presence of a horizontal electric field is investigated in (2+1)-dimensions. The equation governing the evolution of the amplitude of the progressive waves is obtained in the form of a two-dimensional nonlinear Schrödinger equation. A three-wave resonant interaction for nonlinear excitations created from electrohydrodynamic capillary-gravity waves is observed to be possible in a dispersive medium with a self-focusing cubic nonlinearity. Under suitable conditions, the nonlinear envelope equations for the resonant interaction are derived by using multiple scales and inverse scattering methods, and an explicit three-wave soliton solution is discussed. Both the dynamic properties and the modulational instability of finite amplitude electrohydrodynamic wave are studied for the cubic nonlinear Schrödinger equation by means of linearized stability analysis and the nonlinear interaction coefficient. We show that the trajectories in phase space exhibit different behavior with the increase of nonlinear perturbations, and we determine the electric field and wavenumber ranges at which the original point is elliptic or hyperbolic, respectively. It is found also that the presence of the electric field in the equation modifies the nature of wave stability and soliton structures, and that the amplitude and width of the soliton are decreased and increased, respectively, when the electric field value increases.

Keywords: Hydrodynamic stability; Nonlinearity; Electrohydrodynamics (search for similar items in EconPapers)
Date: 2008
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475407003230
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:79:y:2008:i:3:p:242-257

DOI: 10.1016/j.matcom.2007.11.010

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().