  We show that weakly guiding nonlinear waveguides support stable propagation
of rotating spatial solitons (azimuthons). We investigate the role of waveguide
symmetry on the soliton rotation. We find that azimuthons in circular
waveguides always rotate rigidly during propagation and the analytically
predicted rotation frequency is in excellent agreement with numerical
simulations. On the other hand, azimuthons in square waveguides may experience
spatial deformation during propagation. Moreover, we show that there is a
critical value for the modulation depth of azimuthons above which solitons just
wobble back and forth, and below which they rotate continuously. We explain
these dynamics using the concept of energy difference between different
orientations of the azimuthon.

Pattern Formation and Solitons;Optics