Nonlinear modes in finite-dimensional PT-symmetric systems

D. A. Zezyulin, V. V. Konotop

By similarity transformations a parity-time (PT-) symmetric Hamiltonian can be reduced to a Hermitian or to another PT-symmetric Hamiltonian having the same linear spectrum. On an example of a PT-symmetric quadrimer we show that the spectral equivalence of different PT-symmetric and Hermitian systems implies neither similarity of the nonlinear modes nor their stability properties. Even the existence of one-parametric families of nonlinear modes is not guaranteed by the PT symmetry of the underlying linear system. Neither the stability is directly related to the PT symmetry: stable nonlinear modes exist beyond the PT symmetry breaking threshold. A “phase diagram” of a general PT-symmetric quadrimer allows for existence of “triple” points, where three different phases meet. We use graph representation of PT-symmetric networks giving simple illustration of linearly equivalent networks and indicating on their possible experimental design.
Pattern Formation and Solitons (nlin.PS); Optics (physics.optics)

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