“…The influence of the radiating waves on the soliton dynamics was also considered in other works; see, for instance [44,45]. In the considered case without pump and losses the solitons also form a family parametrized by the soliton velocity [46,47] and so one can expect that the recoil from the radiation affects the velocity of the solitons. Indeed, one can see that the recoil due to the four-wave mixing results in a change of the soliton velocity, see Fig.…”