Origin of furrows (gaps) in the (k,ω) spectrum

Determine the physical and mathematical mechanism that produces the primary and secondary furrows (gaps) in the spatiotemporal (k,ω) spectrum of the Schrödinger–Helmholtz equation, which intersect the rectilinear solitonic traces above the primary bound-state trace.

Background

In their analysis of the consolidated bound state using the (k,ω) spectrum, the authors observe not only a primary solitonic trace and sidebands but also distinct furrows that cut traces lying above the primary. These features recur in simulations but remain unexplained.

Understanding these furrows would clarify how coherent structures interact with weak waves in nonintegrable regimes and could illuminate spectral signatures of bound-state dynamics beyond integrable models.

References

Additionally, we note existence of a primary and secondary set of furrows in the $(k,\omega)$ spectrum that cut the rectilinear traces lying above the primary trace. We currently lack any explanation of these gaps in excitation.

— A bound state attractor in optical turbulence (2410.12507 - Colleaux et al., 16 Oct 2024) in Section 3.1–3.2 (Soliton turbulence and the emergence of a bound state)