as azimuthally perturbed optical vortices, i.e. beams with singular phase structure [@coullet_oc_1989; @desyatnikov_prl_2005; @lashkin_pra_2008]. Theoretical studies demonstrated both, stable and unstable propagation of azimuthons [@buccoliero_ol_2008; @lopez-aguayo_oe_2006; @buccoliero_prl_2007], and the first experimental observation of optical azimuthons was recently achieved in rubidium vapors [@minovich_oe_2009].

It appears that higher order solitonic structures and optical vortices are generally unstable in typical nonlinear media with local (Kerr-like) response [@kruglov_jmo_1992; @skryabin_pre_1998]. On the other hand, it has been shown that a spatially nonlocal nonlinear response provides stabilization of various complex solitonic structures including vortices [@suter_pra_1993; @bang_pre_2002; @krolikowski_job_2004; @briedis_oe_2005]. Consequently, azimuthons and their dynamics have been studied almost exclusively in the context of spatially nonlocal nonlinear media [@lopez-aguayo_ol_2006; @buccoliero_prl_2007; @stefan_oe_2008; @Fabian:oqe:09]. In spite of the fact that there are various physical settings exhibiting nonlocality such as nematic liquid crystals [@peccianti_ol_2002; @conti_prl_2003; @conti_prl_2004], Bose-Einstein condensates [@lashkin_pra_2008; @nath_pra_2007; @lashkin_pra_2009], plasmas [@litvak_plasmas_1975], thermo-optical materials [@rotschild_prl_2005] etc., experimental realization of such systems is always quite involved. Moreover, from the theoretical point of view, nonlocal media are quite challenging for numerical modeling and analytical treatment.

In this paper we propose a much simpler and experimentally accessible optical system to study the propagation of azimuthons: a weakly nonlinear optical multi-mode waveguide. Here, weakly 