Discrete-time systems in quasi-standard form and the $\mathfrak{h}_6$ coalgebra symmetry
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914106802438144 |
|---|---|
| author | Drozdov, Pavel Gubbiotti, Giorgio |
| author_facet | Drozdov, Pavel Gubbiotti, Giorgio |
| contents | In this paper, we characterize all discrete-time systems in quasi-standard form admitting coalgebra symmetry with respect to the Lie--Poisson algebra $\mathfrak{h}_{6}$. The outcome of this study is a family of systems depending on an arbitrary function of three variables, playing the rôle of the potential. Moreover, using a direct search approach, we classify discrete-time systems from this family that admit an additional invariant at most quadratic in the physical variables. We discuss the integrability properties of the obtained cases, their relationship with known systems, and their continuum limits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22434 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Discrete-time systems in quasi-standard form and the $\mathfrak{h}_6$ coalgebra symmetry Drozdov, Pavel Gubbiotti, Giorgio Mathematical Physics Exactly Solvable and Integrable Systems 17B80 (Primary) 39A36 (Secondary) In this paper, we characterize all discrete-time systems in quasi-standard form admitting coalgebra symmetry with respect to the Lie--Poisson algebra $\mathfrak{h}_{6}$. The outcome of this study is a family of systems depending on an arbitrary function of three variables, playing the rôle of the potential. Moreover, using a direct search approach, we classify discrete-time systems from this family that admit an additional invariant at most quadratic in the physical variables. We discuss the integrability properties of the obtained cases, their relationship with known systems, and their continuum limits. |
| title | Discrete-time systems in quasi-standard form and the $\mathfrak{h}_6$ coalgebra symmetry |
| topic | Mathematical Physics Exactly Solvable and Integrable Systems 17B80 (Primary) 39A36 (Secondary) |
| url | https://arxiv.org/abs/2410.22434 |