In this paper, we have extended the recently introduced theory of coupled propagation of two coaxially co-propagating and mutually incoherent bright 1-D beams to coupled propagation of two 2-D (cylindrical) bright beams and investigated the propagation behavior and spatial soliton pair formation of such beams by a recently introduced simple approach. We have considered saturable form of the nonlinear medium in this paper as 2-D spatial solitons are unstable in Kerr type media. We found that many of the propagation features of two 2-D beams in saturable media are same that of 1-D beams in Kerr type media. However, many features are different and to the best of our knowledge, reported in this paper for the first time. The present version of the theory is applicable in all possible physical situations and parameters.
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