Higher eigenmodes of nonlocal gap solitons in parity-time symmetric complex potential with a defocusing nonlinearity

The dynamical states have been investigated. The double-hump soliton exists in the PT symmetric domain whereas dies out in the broken PT symmetric region. Linear stability of the double-hump solitons are studied using Bogoliobov-De-Genes equations. The double-hump solitons are unstable and the perturbation modes vary exponentially.