2507.16798
From heteroclinic loops to homoclinic snaking in reversible systems: rigorous forcing through computer-assisted proofs
Jan Bouwe van den Berg, Gabriel William Duchesne, Jean-Philippe Lessard
correctmedium confidence
- Category
- Not specified
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:57 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper rigorously validates (via computer-assisted proofs and a forcing theorem) two interlaced snaking curves for the cubic Swift–Hohenberg (orientable case), an infinite stack of isolas for the same equation (non-orientable case), and snaking for the Gray–Scott model. The candidate solution asserts (B) is false in the reversible Swift–Hohenberg and that (C) remains open, both of which contradict the paper’s verified results.
Referee report (LaTeX)
\textbf{Recommendation:} major revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The paper provides a rigorous, general, and well-executed framework to validate loops of patterned fronts and apply a forcing theorem to obtain global snaking or stacked isolas in reversible 4D systems. The applications to Swift–Hohenberg (snakes and isolas) and Gray–Scott (snakes) are significant. Revisions would improve clarity for the Gray–Scott part (an explicit theorem akin to Theorems 4.2 and 4.3) and consolidate validated bounds/parameters for reproducibility.