The existence and stability of fundamental, dipole, and tripole solitons in Kerr nonlinear media with parity-time symmetric Gaussian complex potentials are reported. Fundamental solitons are stable not only in deep potentials but also in shallow potentials. Dipole and tripole solitons are stable only in deep potentials, and tripole solitons are stable in deeper potentials than for dipole solitons. The stable regions of solitons increase with increasing potential depth. The power of solitons increases with increasing propagation constant or decreasing modulation depth of the potentials.

The existence and stability of defect solitons in parity-time (PT) symmetric optical lattices with nonlocal nonlinearity are reported. It is found that nonlocality can expand the stability region of defect solitons. For positive or zero defects, fundamental and dipole solitons can exist stably in the semi-infinite gap and the first gap, respectively. For negative defects, fundamental solitons can be stable in both the semi-infinite gap and the first gap, whereas dipole solitons are unstable in the first gap. There exist a maximum degree of nonlocal nonlinearity, above which the fundamental solitons in the semi-infinite gap and the dipole solitons in the first gap do not exist for negative defects. The influence of the imaginary part of the PT-symmetric potentials on soliton stability is given. When the modulation depth of the PT-symmetric lattices is small, defect solitons can be stable for positive and zero defects, even if the PT-symmetric potential is above the phase transition point.

Optical solitons in the parity-time (PT)-symmetric Bessel complex potential are studied, including the linear case, and self-focusing and self-defocusing nonlinear cases. For the linear case, the PT-symmetric breaking points, eigenvalues and the eigenfunction for different modulated depths of the PT-symmetric Bessel complex potential are obtained numerically. The PT-symmetric breaking points increase linearly with increasing the real part of the modulated depths of the PT potential. Below the PT-symmetric breaking points, the eigenfunctions of linear modes are symmetrical; however, the symmetries of the eigenfunction break above the PT-symmetric breaking points. For nonlinear cases, the existence and stability of fundamental and multipole solitons are studied in self-focusing and self-defocusing media. The eigenvalue for the linear case is equal to the critical propagation constant bc of the existing soliton. Fundamental solitons are stable in the whole region and multipole solitons are stable with the propagation constants being close to bc both for self-focusing and self-defocusing nonlinearities. The range of solitons’ stability decreases with an increase of the number of the intensity peaks of the solitons.