Spatial solitons with the odd and even symmetries in (2+1)-dimensional spatially inhomogeneous cubic-quintic nonlinear media with transverse W-shaped modulation

We firstly investigate analytical spatial soliton solutions with the odd and even symmetries in (2+1)-dimensional spatially inhomogeneous cubic-quintic nonlinear media considering transverse W-shaped modulation. The power of localized states increases one by one along the line y = x when the soliton order number n increases. The stability analysis and numerical calculations show that stable fundamental solitons exist while higher order solitons are unstable in three nonlinear media, i.e. the defocusing cubic and focusing quintic nonlinear medium, focusing cubic and defocusing quintic nonlinear medium, and focusing cubic and focusing quintic nonlinear medium. While all solitons (even fundamental solitons) are unstable and ultimately decay into noise in the defocusing cubic and defocusing quintic nonlinear medium.