A two-dimensional paradigm for symmetry breaking: the nonlinear Schrodinger equation with a four-well potential

Abstract

We study the existence and stability of localized states in the two-dimensional (2D) nonlinear Schrodinger (NLS)/Gross-Pitaevskii equation with a symmetric four-well potential. Using a fourmode approximation, we are able to trace the parametric evolution of the trapped stationary modes, starting from the corresponding linear limits, and thus derive the complete bifurcation diagram for the families of these stationary modes. The predictions based on the four-mode decomposition are found to be in good agreement with the numerical results obtained from the NLS equation. Actually, the stability properties coincide with those suggested by the corresponding discrete model in the large-amplitude limit. The dynamics of the unstable modes is explored by means of direct simulations. Finally, while we present the full analysis for the case of the focusing nonlinearity, the bifurcation diagram for the defocusing case is briefly considered too.

11 pages, 10 figures

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• Experimental observation of oscillating and interacting matter wave dark solitons
• Spontaneous symmetry breaking in a nonlinear double-well structure
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• Spontaneous soliton symmetry breaking in two-dimensional coupled Bose-Einstein condensates supported by optical lattices
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• High-Order-Mode Soliton Structures in Two-Dimensional Lattices with Defocusing Nonlinearity
• Light bullets in Bessel optical lattices with spatially modulated nonlinearity
• Stabilization of two-dimensional solitons and vortices against supercritical collapse by lattice potentials
• Stability of Quantized Vortices in a Bose-Einstein Condensate Confined in an Optical Lattice

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• Symmetry breaking of spatial Kerr solitons in fractional dimension
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• Stability analysis for pitchfork bifurcations of solitary waves in generalized nonlinear Schroedinger equations
• Dark solitons in cigar-shaped Bose-Einstein condensates in double-well potentials
• Spontaneous symmetry breaking of photonic and matter waves in two-dimensional pseudopotentials
• Spontaneous symmetry breaking in linearly coupled disk-shaped Bose-Einstein condensates
• Nonlinear Schrodinger equations with multiple-well potential
• Coherence oscillations between weakly coupled Bose-Hubbard dimers
• Symmetry breaking in binary chain with nonlinear sites
• Effects of Long-Range Nonlinear Interactions in Double-Well Potentials
• Stability switching at transcritical bifurcations of solitary waves in generalized nonlinear Schroedinger equations
• Nonlinear Waves in an Experimentally Motivated Ring-shaped Bose-Einstein Condensate Setup
• Efficient Manipulation of Bose-Einstein Condensates in a Double-Well Potential
• Symmetry-breaking Effects for Polariton Condensates in Double-Well Potentials
• Stationary solutions for multi-dimensional Gross-Pitaevskii equation with double-well potential
• Spontaneous symmetry-breaking in the nonlinear Schrödinger equation on star graphs with inhomogeneities
• Spontaneous Symmetry Breaking In Nonlinear Binary Periodic Systems