PreprintCC BY 4.0arXiv
H-integrable solutions to 2d dimensional canonical systems
Abstract
In this paper we study 2d-dimensional canonical systems with positive semidefinite Hamiltonians H(t) satisfying tr H(t) ≡ 1. We first establish that every such system possesses at least one nontrivial H-integrable solution, ensuring the existence of solutions whose energy with respect to H remains finite. We then show that the space of all H-integrable solutions has dimension at most d.
Related
- Deformations of (2+1)-dimensional integrable systems and isotropic and anisotropic Harry Dym variants
- A complete classification of the existence of finite-dimensional quantum solutions to inconsistent linear constraint systems
- Flexibility of two-dimensional Euler flows with integrable vorticity
- Integrable and non-integrable LR geodesic flows on 5-dimensional 2-step nilpotent Lie groups
- On Integrable Deformations of CFTs and Integrable Two-Dimensional Sigma Models
BibTeX
@misc{acharya2026hintegrable,
title = {{H-integrable solutions to 2d dimensional canonical systems}},
author = {Keshav Raj Acharya},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13208},
eprint = {2609.13208},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13208},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - H-integrable solutions to 2d dimensional canonical systems
AU - Keshav Raj Acharya
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.13208
UR - https://arxiv.org/abs/2609.13208
AB - In this paper we study 2d-dimensional canonical systems with positive semidefinite Hamiltonians H(t) satisfying tr H(t) ≡ 1. We first establish that every such system possesses at least one nontrivial H-integrable solution, ensuring the existence of solutions whose energy with respect to H remains finite. We then show that the space of all H-integrable solutions has dimension at most d.
ER -