In this paper, we investigate the existence of moving solitons in the model proposed in Ref. [5]. Using the relaxation technique we have been able to obtain moving soliton solutions. The stability of these solitons are investigated numerically. A key finding is that for fixed parameters the stability borders depend on the velocity of solitons and detuning frequency. We have also considered the collision of counterpropagating in-phase and π-out-of-phase moving solitons in this model.
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