Domain walls and vortices in linearly coupled systems
- Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv IL-69978 (Israel)
We investigate one- and two-dimensional radial domain-wall (DW) states in the system of two nonlinear-Schroedinger (NLS) or Gross-Pitaevskii (GP) equations, which are couple by linear mixing and by nonlinear XPM (cross-phase-modulation). The system has straightforward applications to two-component Bose-Einstein condensates, and to bimodal light propagation in nonlinear optics. In the former case the two components represent different hyperfine atomic states, while in the latter setting they correspond to orthogonal polarizations of light. Conditions guaranteeing the stability of flat continuous wave (CW) asymmetric bimodal states are established, followed by the study of families of the corresponding DW patterns. Approximate analytical solutions for the DWs are found near the point of the symmetry-breaking bifurcation of the CW states. An exact DW solution is produced for ratio 3:1 of the XPM and SPM (self-phase modulation) coefficients. The DWs between flat asymmetric states, which are mirror images of each other, are completely stable, and all other species of the DWs, with zero crossings in one or two components, are fully unstable. Interactions between two DWs are considered too, and an effective potential accounting for the attraction between them is derived analytically. Direct simulations demonstrate merger and annihilation of the interacting DWs. The analysis is extended for the system including single- and double-peak external potentials. Generic solutions for trapped DWs are obtained in a numerical form, and their stability is investigated. An exact stable solution is found for the DW trapped by a single-peak potential. In the 2D geometry, stable two-component vortices are found, with topological charges s=1,2,3. Radial oscillations of annular DW-shaped pulsons, with s=0,1,2, are studied too. A linear relation between the period of the oscillations and the mean radius of the DW ring is derived analytically.
- OSTI ID:
- 21612140
- Journal Information:
- Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print), Vol. 84, Issue 4; Other Information: DOI: 10.1103/PhysRevE.84.046602; (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 1539-3755
- Country of Publication:
- United States
- Language:
- English
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GENERAL PHYSICS
ANALYTICAL SOLUTION
ANNIHILATION
APPROXIMATIONS
ASYMMETRY
BIFURCATION
BOSE-EINSTEIN CONDENSATION
COMPUTERIZED SIMULATION
DOMAIN STRUCTURE
EQUATIONS
GEOMETRY
LIGHT TRANSMISSION
MODULATION
NONLINEAR OPTICS
NONLINEAR PROBLEMS
OSCILLATIONS
POLARIZATION
POTENTIALS
SYMMETRY BREAKING
TOPOLOGY
TWO-DIMENSIONAL CALCULATIONS
CALCULATION METHODS
INTERACTIONS
MATHEMATICAL SOLUTIONS
MATHEMATICS
OPTICS
PARTICLE INTERACTIONS
SIMULATION
TRANSMISSION