Azimuthally modulated ring solitons in Bessel photonic lattices

Energy spectrum, stability and internal modes of azimuthally modulated ring solitons are investigated in defocusing photorefractive crystal with imprinted Bessel photonic lattices. It is shown that internal modes of the azimuthally modulated ring solitons may have both real parts and imaginary parts. If there exists internal modes of the stable azimuthally modulated ring solitons, the solitons perform long-distance and quasi-periodic oscillation of intensity and shape under the perturbation of internal modes.