Breathing spatial solitons in non-Kerr media

The concept of soliton internal mode is introduced to explain quantitatively the long-lived oscillations of self-guided beams, or breathing spatial solitons. Cubic-quintic nonlinearity is considered in detail, and it is shown that the existence of the internal mode affects strongly the beam propagation in non-Kerr media, leading to oscillatory dependence of the output width of the beam versus its input power.