Abstract
We report on the existence and stability of nonlocal multihump gap solitons in one-dimensional parity-time symmetric periodic potentials. They can exist in the first gap in defocusing nonlocal nonlinearity and in the semi-infinite gap in focusing nonlocal nonlinearity. These solitons can be stable in the defocusing nonlinearity but are unstable in the focusing nonlinearity. For the multihump solitons, the shapes of the nonlinear contribution to refractive index are also multihump. The stability and shapes of the intensity distribution of these solitons will be changed by the degree of nonlocality. We also study the transverse power flow of these solitons.
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