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The real spectrum of bound states produced by PT-symmetric Hamiltoniansusually suffers breakup at a critical value of the strength of gain-loss terms,i.e., imaginary part of the complex potential. On the other hand, it is knownthat the PT-symmetry can be made unbreakable in a one-dimensional (1D) modelwith self-defocusing nonlinearity whose strength grows fast enough from thecenter to periphery. The model is nonlinearizable, i.e., it does not have alinear spectrum, while the (unbreakable) PT symmetry in it is defined byspectra of continuous families of nonlinear self-trapped states (solitons).Here we report results for a 2D nonlinearizable model whose PT symmetry remainsunbroken for arbitrarily large values of the gain-loss coeffcient. Further, weintroduce an extended 2D model with the imaginary part of potential ~ xy in theCartesian coordinates. The latter model is not a PT-symmetric one, but it alsosupports continuous families of self-trapped states, thus suggesting anextension of the concept of the PT symmetry. For both models, universalanalytical forms are found for nonlinearizable tails of the 2D modes, and fullexact solutions are produced for particular solitons, including ones with theunbreakable PT symmetry, while generic soliton families are found in anumerical form. The PT-symmetric system gives rise to generic families ofstable single- and double-peak 2D solitons (including higher-order radialstates of the single-peak solitons), as well as families of stable vortexsolitons with winding numbers m = 1, 2, and 3. In the model with imaginarypotential ~ xy, families of single-and multi-peak solitons and vortices arestable if the imaginary potential is subject to spatial confinement. In anelliptically deformed version of the latter model, an exact solution is foundfor vortex solitons with m = 1.

Robust PT symmetry of two-dimensional fundamental and vortex solitons supported by spatially modulated nonlinearity