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We introduce one- and two-dimensional (1D and 2D) models of parity-time ($%\mathcal{PT}$) -symmetric couplers with the mutually balanced linear gain andloss applied to the two cores, and cubic-quintic (CQ) nonlinearity acting ineach one. The 2D and 1D models may be realized in dual-core optical waveguides,in the spatiotemporal and spatial domains, respectively. Stationary solutionsfor $\mathcal{PT}$-symmetric solitons in these systems reduce to theircounterparts in the usual coupler. The most essential problem is the stabilityof the solitons, which become unstable against symmetry breaking with theincrease of the energy (norm), and retrieve the stability at still largerenergies. The boundary value of the intercore-coupling constant, above whichthe solitons are completely stable, is found by means of an analyticalapproximation, based on the CW (zero-dimensional) counterpart of the system.The approximation demonstrates good agreement with numerical findings for the1D and 2D solitons. Numerical results for the stability limits of the 2Dsolitons are obtained by means of the computation of eigenvalues for smallperturbations, and verified in direct simulations. Although large parts of thesolitons families are unstable, the instability is quite weak. Collisionsbetween 2D solitons in the $\mathcal{PT}$-symmetric coupler are studied bymeans of simulations. Outcomes of the collisions are inelastic but notdestructive, as they do not break the $\mathcal{PT}$ symmetry.

Stability boundaries and collisions of two-dimensional solitons in PT-symmetric couplers with the cubic-quintic nonlinearity