Multipole solitons in competing nonlinear media with an annular potential

We address the existence, stability, and propagation dynamics of multipole-mode solitons in cubic-quintic nonlinear media with an imprinted annular (ring-shaped) potential. The interplay of the competing nonlinearity with the potential enables the formation of a variety of solitons with complex structures, from dipole, quadrupole, and octupole solitons to necklace complexes. The system maintains two branches of soliton families with opposite slopes of the power-vs.-propagation-constant curves. While the solitons' stability domain slowly shrinks with the increase of even number n of lobes in the multipole patterns, it remains conspicuous even for n > 16. The application of a phase torque gives rise to stable rotation of the soliton complexes, as demonstrated by means of analytical and numerical methods.