Abstract
We show analytically and numerically that time delayed nonlocal response induces traveling localized states in bistable systems. These states result from fronts interaction. We illustrate this mechanism in a generic bistable model with a nonlocal delayed response. Analytical expression of the width and the speed of traveling localized states are derived. Without time delayed nonlocal response traveling localized states are excluded. Finally, we consider an experimentally relevant system, the fiber cavity with the non-instantaneous Raman response, and show evidence of traveling localized state. In addition, we propose realistic parameters and perform numerical simulations of the governing model equation.
Highlights
Macroscopic systems are regularly described by a small number of coarse-grained or macroscopic variables
IV, we show analytically and numerically that delayed nonlocal response through front interaction allows for the stabilization moving localized structures
We have shown analytically and numerically that nonlocal delayed response in the form of the Raman effect stabilizes traveling localized structures
Summary
Macroscopic systems are regularly described by a small number of coarse-grained or macroscopic variables. Frequency combs generated in optical Kerr resonators are nothing but the spectral content of the stable temporal localized structure (LS) occurring in the cavity [12,13]. These peaks are generated close to the modulational instability. The formation of traveling localized structures induced by the time-delayed response, including the Raman effect, have neither been experimentally determined nor theoretically predicted. The paper is organized as follows: In Sec. II, we present a generalized Lugiato-Lefever model describing all-fiber resonators with Raman delayed nonlocal response, and we show numerical evidence of moving localized structures.
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