Time-delayed nonlocal response inducing traveling temporal localized structures

Abstract

We show analytically and numerically that time-delayed nonlocal response induces traveling localized states in bistable systems. These states result from the interaction of fronts between homogeneous steady states. We illustrate this mechanism by considering an experimentally relevant system—the fiber cavity with the noninstantaneous Raman response. Close to the nascent bistability, we performed a derivation of a generic bistable model with a nonlocal delayed response. Analytical expressions of the width and the speed of traveling localized states are derived. Without a time-delayed nonlocal response, traveling localized states are excluded. In addition, we propose realistic parameters and perform numerical simulations of the governing model equation.