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Nonlinear Modes and Symmetries in Linearly Coupled Pairs of PT ‐Invariant Dimers
Author(s) -
Li K.,
Kevrekidis P. G.,
Malomed B. A.
Publication year - 2014
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12038
Subject(s) - antisymmetric relation , physics , invariant (physics) , decoupling (probability) , homogeneous space , bifurcation , nonlinear system , symmetry breaking , saddle point , work (physics) , classical mechanics , mathematics , quantum mechanics , mathematical physics , geometry , control engineering , engineering
The subjects of the work are pairs of linearly coupled PT ‐symmetric dimers. Two different settings are introduced, namely, straight‐coupled dimer s, where each gain site is linearly coupled to one gain and one loss site, and cross‐coupled dimers , with each gain site coupled to two lossy ones. The latter pair with equal coupling coefficients represents a PT ‐ hypersymmetric quadrimer. We find symmetric and antisymmetric solutions in these systems, chiefly in an analytical form, and explore the existence, stability, and dynamical behavior of such solutions by means of numerical methods. We thus identify bifurcations occurring in the systems, including spontaneous symmetry breaking and saddle‐center bifurcations. Simulations demonstrate that evolution of unstable branches typically leads to blowup. However, in some cases, unstable modes rearrange into stable ones.