TY - JOUR
T1 - Spontaneous symmetry breaking of binary fields in a nonlinear double-well structure
AU - Acus, Arturas
AU - Malomed, Boris A.
AU - Shnir, Yakov
N1 - Funding Information:
A.A. acknowledges support by the EU FP7 project STREP NAMEQUAM and Ya S acknowledges support from the A von Humboldt Foundation .
PY - 2012/6/1
Y1 - 2012/6/1
N2 - We introduce a one-dimensional two-component system with the self-focusing cubic nonlinearity concentrated at a symmetric set of two spots. Effects of the spontaneous symmetry breaking (SSB) of localized modes were previously studied in the single-component version of this system. In this work, we study the evolution (in the configuration space of the system) and SSB scenarios for two-component modes of three generic types, as concerns the spatial symmetry of each component: symmetricsymmetric (SmSm), antisymmetricantisymmetric (ASAS), and symmetricantisymmetric (SAS) ones. In the limit case of the nonlinear potential represented by two δ-functions, solutions are obtained in a semi-analytical form. They feature novel properties, in comparison with the previously studied single-component model. In particular, the SSB of antisymmetric modes is possible solely in the two-component system, and, obviously, SAS states exist only in the two-component system too. In the general case of the symmetric pair of finite-width nonlinear potential wells, evolution scenarios are very complex. In this case, new results are reported, first, for the single-component model. These are pairs of broken-antisymmetry modes, and of twin-peak symmetric ones, which are generated by saddle-mode bifurcations separated from the transformations previously studied in the single-component setting. With regard to these findings, complex scenarios of the evolution of the two-component solution families are realized in terms of links connecting pairs of modes of three simplest types: (A) two-component ones with unbroken symmetries; (B) single-component modes featuring density peaks in both potential wells; (C) single-component modes which are trapped, essentially, in a single well.
AB - We introduce a one-dimensional two-component system with the self-focusing cubic nonlinearity concentrated at a symmetric set of two spots. Effects of the spontaneous symmetry breaking (SSB) of localized modes were previously studied in the single-component version of this system. In this work, we study the evolution (in the configuration space of the system) and SSB scenarios for two-component modes of three generic types, as concerns the spatial symmetry of each component: symmetricsymmetric (SmSm), antisymmetricantisymmetric (ASAS), and symmetricantisymmetric (SAS) ones. In the limit case of the nonlinear potential represented by two δ-functions, solutions are obtained in a semi-analytical form. They feature novel properties, in comparison with the previously studied single-component model. In particular, the SSB of antisymmetric modes is possible solely in the two-component system, and, obviously, SAS states exist only in the two-component system too. In the general case of the symmetric pair of finite-width nonlinear potential wells, evolution scenarios are very complex. In this case, new results are reported, first, for the single-component model. These are pairs of broken-antisymmetry modes, and of twin-peak symmetric ones, which are generated by saddle-mode bifurcations separated from the transformations previously studied in the single-component setting. With regard to these findings, complex scenarios of the evolution of the two-component solution families are realized in terms of links connecting pairs of modes of three simplest types: (A) two-component ones with unbroken symmetries; (B) single-component modes featuring density peaks in both potential wells; (C) single-component modes which are trapped, essentially, in a single well.
KW - Bifurcations
KW - BoseEinstein condensate in two-component systems
KW - GrossPitaevskii equation
KW - Nonlinear Schroedinger equation
KW - Self-focusing cubic nonlinearity
KW - Spontaneous symmetry breaking
UR - http://www.scopus.com/inward/record.url?scp=84859431032&partnerID=8YFLogxK
U2 - 10.1016/j.physd.2012.02.012
DO - 10.1016/j.physd.2012.02.012
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AN - SCOPUS:84859431032
SN - 0167-2789
VL - 241
SP - 987
EP - 1002
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 11
ER -