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Two-dimensional paradigm for symmetry breaking : the nonlinear Schrödinger equation with a four-well potential
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Wang, C., Theocharis, G., Kevrekidis, P., Whitaker, N., Law, K. J. H., Frantzeskakis, D. and Malomed, B. (2009) Two-dimensional paradigm for symmetry breaking : the nonlinear Schrödinger equation with a four-well potential. Physical Review E, Vol.80 (No.4). Article no. 046611 . doi:10.1103/PhysRevE.80.046611 ISSN 1539-3755.
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Official URL: http://dx.doi.org/10.1103/PhysRevE.80.046611
Abstract
We study the existence and stability of localized modes in the two-dimensional (2D) nonlinear Schrödinger/Gross-Pitaevskii (NLS/GP) equation with a symmetric four-well potential. Using the corresponding four-mode approximation, we trace the parametric evolution of the trapped stationary modes, starting from the linear limit, and thus derive a complete bifurcation diagram for families of the stationary modes. This provides the picture of spontaneous symmetry breaking in the fundamental 2D setting. In a broad parameter region, the predictions based on the four-mode decomposition are found to be in good agreement with full numerical solutions of the NLS/GP equation. Stability properties of the stationary states coincide with those suggested by the corresponding discrete model in the large-amplitude limit. The dynamics of unstable modes is explored by means of direct simulations. Finally, in addition to the full analysis for the case of the self-attractive nonlinearity, the bifurcation diagram for the case of self-repulsion is briefly considered too.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Physical Review E | ||||
Publisher: | American Physical Society | ||||
ISSN: | 1539-3755 | ||||
Official Date: | 2009 | ||||
Dates: |
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Volume: | Vol.80 | ||||
Number: | No.4 | ||||
Page Range: | Article no. 046611 | ||||
DOI: | 10.1103/PhysRevE.80.046611 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published |
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