2504.10729
On novel Hamiltonian descriptions of some three-dimensional non-conservative systems
Aritra Ghosh, Anindya Ghose-Choudhury, Partha Guha
correctmedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper’s claims and computations (resistive-Hamiltonian realizations, the JR+RJ Poisson test in Proposition 4.1, explicit bi-Hamiltonian construction for the reduced three-wave model, and conformal Hamiltonian descriptions) are borne out by direct calculation. The candidate solution reproduces the same verifications, occasionally with different but valid J,R choices that yield the same dynamics, and it explicitly carries out the characteristic integration for G and M. Notably, the paper contains a minor typographical error in the bi-Hamiltonian cross-product formula (they write ∇G×∇G where the second Hamiltonian should be the other one), which the model corrects by using M ẋ = ∇G×∇H. Aside from this small slip, the arguments match in substance.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The paper correctly unifies several 3D systems within resistive-Hamiltonian, bi-Hamiltonian, and conformal Hamiltonian frameworks and backs claims with explicit computations. A small typographical error in the bi-Hamiltonian cross-product formula should be corrected. Clarifying the non-uniqueness of (J,R) and the locality of (G,M) would improve rigor and readability. Overall, the results are sound and useful for specialists in Poisson/Nambu and port-Hamiltonian systems.