Dynamics of a chain of interacting parity-time invariant nonlinear dimers is
investigated. A dimer is built as a pair of coupled elements with equal gain
and loss. A relation between stationary soliton solutions of the model and
solitons of the discrete nonlinear Schrodinger (DNLS) equation is demonstrated.
Approximate solutions for solitons whose width is large in comparison to the
lattice spacing are derived, using a continuum counterpart of the discrete
equations. These solitons are mobile, featuring nearly elastic collisions.
Stationary solutions for narrow solitons, which are immobile due to the pinning
by the effective Peierls-Nabarro potential, are constructed numerically,
starting from the anti-continuum limit. The solitons with the amplitude
exceeding a certain critical value suffer an instability leading to blowup,
which is a specific feature of the nonlinear PT-symmetric chain, making it
dynamically different from DNLS lattices. A qualitative explanation of this
feature is proposed. The instability threshold drops with the increase of the
gain-loss coefficient, but it does not depend on the lattice coupling constant,
nor on the soliton's velocity.Comment: 9 pages, 9 figure
