Optical dispersive shock waves of initial pulses in optical fibers with high-order dispersion and quintic nonlinearity effects

Abstract

This paper probes the dispersive shock waves (DSWs) theory in nonlinear optical systems through Whitham modulation theory for the high-order Chen-Lee-Liu (HOCLL) equation. We systematically derived the one-phase periodic solutions and the corresponding Whitham equations. For all feasible initial discontinuous conditions, we delineate a classification of wave structures during the evolutionary process by virtue of the initial distribution of Riemann invariants, including both convex and non-convex cases. In this classification, we find that the evolved wave structures in non-convex cases incorporate an additional and more complex region-contact DSW region, compared with those in convex cases. So we analyze the propagation behavior of this region. Additionally, we also take into account the problem that the initial wave at the instant of wave breaking approximated by the cubic root function, and elaborately analyze the propagation of photons in optical fibers under the effects of high-order dispersion and quintic nonlinearity.