State Transition Induced by Higher-order Effects and Background Frequency

Abstract

State transition between the Peregrine rogue wave and w-shaped traveling wave induced by higher-order effects and background frequency is studied. We find that this intriguing transition, described by an exact explicit rational solution, is consistent with the modulation instability (MI) analysis that involves MI region and stability region in low perturbation frequency region. In particular, the link between the MI growth rate and transition characteristic analytically demonstrates that, the size characteristic of transition is positively associated with the reciprocal of zero-frequency growth rate. Further, we investigate the case for nonlinear interplay of multi-localized waves. It is interesting that the interaction of second-order waves in stability region features a line structure, rather than an elastic interaction between two w-shaped traveling waves.

5 pages, 8 figures

References in corpus (2)

• Instabilities, breathers and rogue waves in optics
• Vector Rogue Waves and Baseband Modulation Instability in the Defocusing Regime

Cited by in corpus (5)

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• Controllable generations of several nonlinear waves in optical fibers with third-order dispersion
• Characteristics of optical multi-peak solitons induced by higher-order effects in an erbium-doped fiber system
• Femtosecond Optical Superregular Breathers
• The three-level coupled Maxwell-Bloch equations: rogue waves, semirational rogue waves and W-shaped solitons