Bragg soliton is a solution of the nonlinear coupled mode equations (NLCMEs) that are a non-integrable system. Nevertheless, we show that for a broad region of soliton parameters the interaction between two Bragg solitons in a uniform fiber Bragg grating can be accurately described by using a trial function based on the known solution for two-soliton interaction in the massive Thirring model (MTM). In this region the similar behavior of Bragg solitons and solitons of the Thirring model enables one to calculate explicitly the approximate asymptotic properties of the interaction between two Bragg solitons such as the shifts in locations and phases of the solitons as a result of the interaction. We have validated that the similar behavior of Bragg solitons and solitons of the MTM is obtained for a broad range of parameters of the interacting solitons that can also be realized experimentally. Since the NLCMEs are not an integrable system, there is a parameter regime in which the interaction between Bragg solitons does not resemble the elastic interaction between MTM solitons. We describe an interaction between two co-propagating Bragg solitons that causes the inversion of the propagation direction of one of the solitons.
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