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We study symmetric and asymmetric optical multi-peak solitons on a continuouswave background in the femtosecond regime of a single-mode fiber. Keycharacteristics of such multi-peak solitons, as the formation mechanism,propagation stability, and shape-changing collisions, are revealed in detail.Our results show that this multi-peak (symmetric or asymmetric) mode could beregarded as a single pulse formed by a nonlinear superposition of a periodicwave and a single-peak (W-shaped or antidark) soliton. In particular, a phasediagram for different types of nonlinear excitations on a continuous wavebackground including breather, rogue wave, W-shaped soliton, antidark soliton,periodic wave, and multi-peak soliton is established based on the explicit linkbetween exact nonlinear wave solution and modulation instability analysis.Numerical simulations are performed to confirm the propagation stability of themulti-peak solitons with symmetric and asymmetric structures. Further, weunveil a remarkable shape-changing feature of asymmetric multi-peak solitons.It is interesting that these shape-changing interactions occur not only in theintraspecific collision (soliton mutual collision) but also in theinterspecific interaction (soliton-breather interaction). Our resultsdemonstrate that each multi-peak soliton exhibits the coexistence of shapechange and conservation of the localized energy of light pulse against thecontinuous wave background.

Symmetric and asymmetric optical multi-peak solitons on a continuous wave background in the femtosecond regime