Families of fundamental and vortex solitons under competing cubic-quintic nonlinearity with complex potentials

We investigate the properties of two-dimensional(2D) fundamental and vortex solitons propagating in PT symmetric lattices with the competing cubic-quintic nonlinearity. We discuss the influence of the competing nonlinearity and the gain-loss coefficient on the existence and stability of both 2D fundamental solitons and vortex solitons, and obtain the existence and stability ranges of them. The stability of solitons under different competing CQ nonlinearity is analyzed by using the VK criterion or the anti-VK criterion. We demonstrate that the whole nonlinearity is determined by the coefficients of nonlinear terms and the propagation constants of solitons. In particular, the power curve of vortex soliton leap and move back near the Bloch band instead of bifurcating from it under the defocusing cubic and focusing quintic nonlinearity.