Stationary coupled KdV systems and their Stäckel representations
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914763116642304 |
|---|---|
| author | Szablikowski, Błażej M. Błaszak, Maciej Marciniak, Krzysztof |
| author_facet | Szablikowski, Błażej M. Błaszak, Maciej Marciniak, Krzysztof |
| contents | In this article we investigate stationary cKdV systems and prove that every $N$-field stationary cKdV system can be written, after a careful reparametrization of jet variables, as a classical separable Stäckel system on $N+1$ different ways. For each of these $N+1$ parametrizations we present an explicit map between the jet variables and the separation variables of the system. Finally, we show that each pair of Stäckel representations of the same stationary cKdV system, when considered in the phase space extended by Casimir variables, is connected by an appropriate finite-dimensional Miura map, which leads to an $(N+1)$-Hamiltonian formulation for the stationary cKdV system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_02282 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stationary coupled KdV systems and their Stäckel representations Szablikowski, Błażej M. Błaszak, Maciej Marciniak, Krzysztof Exactly Solvable and Integrable Systems Mathematical Physics In this article we investigate stationary cKdV systems and prove that every $N$-field stationary cKdV system can be written, after a careful reparametrization of jet variables, as a classical separable Stäckel system on $N+1$ different ways. For each of these $N+1$ parametrizations we present an explicit map between the jet variables and the separation variables of the system. Finally, we show that each pair of Stäckel representations of the same stationary cKdV system, when considered in the phase space extended by Casimir variables, is connected by an appropriate finite-dimensional Miura map, which leads to an $(N+1)$-Hamiltonian formulation for the stationary cKdV system. |
| title | Stationary coupled KdV systems and their Stäckel representations |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics |
| url | https://arxiv.org/abs/2305.02282 |