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Abstract
In this paper, we focus on the on-axis intensity evolutions of hollow beams in nonlinear media with a high nonlocality. It is found that, the evolutions of on-axis intensity with different beam powers are always periodic during propagation, whereas, depending on different beam powers, the evolution curves of on-axis intensity in each period may exhibit themselves as three different types, namely, a concave, a platform, or a convex shape. The critical power, the extreme values of on-axis intensity and their corresponding positions are all given analytically.
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