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V.V. Konotop, D.E. Pelinovsky, and D.A. Zezyulin,

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Discrete solitons in PT-symmetric lattices

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**Abstract:**

We prove existence of discrete solitons in infinite parity-time (PT-) symmetric lattices
by means of analytical continuation from the anticontinuum limit. The energy balance between
dissipation and gain implies that in the anticontinuum limit the solitons are constructed from
elementary PT-symmetric blocks such as dimers, quadrimers, or more general oligomers. We
consider in detail a chain of coupled dimers, analyze bifurcations of discrete solitons from the
anticontinuum limit and show that the solitons are stable in a sufficiently large region of the
lattice parameters. The generalization of the approach is illustrated on two examples of networks
of quadrimers, for which stable discrete solitons are also found.

**Keywords:**

Localized modes, PT-symmetries, discrete nonlinear Schrodinger equation, anti-continuum limit,
existence and stability