We theoretically reveal the link between two types of self-acceleration mechanisms widely emerging in wave dynamics and experimentally demonstrate such a connection via pulse interactions in nonlinear optical fibers. We find that, in order to realize a pulse pair subjected to a diametric drive acceleration, one of the two components can be directly obtained from a self-accelerating Airy-like pulse under appropriate conditions. Such a form of synchronized acceleration cannot be achieved by approaches previously used to generate diametric drive acceleration. Our results generalize the fundamental concept of diametric drive acceleration and may bring about unconventional approaches to control self-accelerating waves.
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