Dynamics of PT-asymmetric multi-peak solitons with complex potentials

We investigate the existence and stability of two-dimensional PT-asymmetric multi-peak solitons in the PT-symmetric potentials, which imaginary part quasi-one-dimensional, based on the self-defocusing cubic nonlinearity. It is found that the in-phase multi-peak solitons with both even and odd number of peaks can stably exist in some regions of the first gap, but these regions are piecewise for some multi-peak solitons. The imaginary part of the potential can dramatically affect the existence and stability of these in-phase PT-asymmetric solitons. The out-of-phase PT-asymmetric multi-peak solitons are unstable in their whole existence regions. In addition, the asymmetry of these solitons is investigated in detail. The properties of PT-symmetric one-, two-, rhombic four and five-peak solitons are also analysed. It is found that the one-, two- and five-peak solitons can be stable in a wide region, while four-peak solitons are unstable in their whole existence regions.