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.

arXiv comment11 pages, 10 figures

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• Dark solitons in cigar-shaped Bose-Einstein condensates in double-well potentials
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• 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
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• 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