Rigorous construction of normal-dispersion frequency combs under constant forcing

Construct soliton-based frequency-comb solutions of the Lugiato–Lefever equation in the normal-dispersion regime when the forcing function is constant.

Background

The paper constructs dark pulse and frequency-comb solutions in the normal-dispersion regime for genuinely periodic forcing. It contrasts this result with the constant-forcing case, where prior rigorous constructions exist in the anomalous-dispersion regime but not in the normal-dispersion regime. The authors explicitly identify the latter construction as unresolved.

References

To the best of the authors' knowledge, the rigorous construction of soliton-based frequency combs for~eq:LLE in the normal dispersion regime remains an open problem in the case of constant forcing.

— Dissipative bright and dark pulses under periodic forcing  (2608.14077 - Bengel et al., 14 Aug 2026) in Introduction, Remark following the discussion of constant forcing