Oscillatory motion of dissipative solitons induced by delay-feedback in inhomogeneous Kerr resonators

A B S T R A C T We investigate the destabilization mechanisms of dissipative solitons in inhomogeneous nonlinear res-onators subjected to injection and to time-delayed feedback. We consider the paradigmatic Lugiato-Lefever model describing inhomogeneous driven nonlinear optical resonator. We analyze the pinning-depinning transition of dissipative solitons by introducing a potential induced by the inhomogeneity. Fur-ther, we identify conditions under which these structures are destabilized and describe different bifurca-tion scenarios. We show that the combined influence of inhomogeneities and delayed feedback induces an Andronov-Hopf-bifurcation that leads to oscillations of the dissipative soliton around the inhomogene-ity. Finally, we show that for large values of the feedback strength, the dissipative solitons escapes from the potential well and starts to drift. (c) 2021 Elsevier Ltd. All rights reserved.