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We analyze a system of three two-dimensional nonlinear Schr\"odingerequations coupled by linear terms and with the cubic-quintic(focusing-defocusing) nonlinearity. We consider two versions of the model:conservative and parity-time ($\mathcal{PT}$) symmetric. These models describetriple-core nonlinear optical waveguides, with balanced gain and losses in the$\mathcal{PT}$-symmetric case. We obtain families of soliton solutions anddiscuss their stability. The latter study is performed using a linear stabilityanalysis and checked with direct numerical simulations of the evolutionalsystem of equations. Stable solitons are found in the conservative and$\mathcal{PT}$-symmetric cases. Interactions and collisions between theconservative and $\mathcal{PT}$-symmetric solitons are briefly investigated, aswell.

Two-dimensional solitons in conservative and parity-time-symmetric triple-core waveguides with cubic-quintic nonlinearity