Solitons in parity-time symmetric potentials with spatially modulated nonlocal nonlinearity.

We study the solitons in parity-time symmetric potential in the medium with spatially modulated nonlocal nonlinearity. It is found that the coefficient of the spatially modulated nonlinearity and the degree of the uniform nonlocality can profoundly affect the stability of solitons. There exist stable solitons in low-power region, and unstable solitons in high-power region. In the unstable cases, the solitons exhibit jump from the original site to the next one, and they can continue the motion into the other lattices. The region of the stable soliton can be expanded by increasing the coefficient of the modulated nonlocality. Finally, critical amplitude of the imaginary part of the linear PT lattices is obtained, above which solitons are unstable and decay immediately.