On integrability of a new dynamical system associated with the BBM-type hydrodynamic flow
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910522512769024 |
|---|---|
| author | Dutykh, Denys Prykarpatskyy, Yarema A. |
| author_facet | Dutykh, Denys Prykarpatskyy, Yarema A. |
| contents | This article explores the exceptional integrability property of a family of higher-order Benjamin-Bona-Mahony (BBM)-type nonlinear dispersive equations. Here, we highlight its deep relationship with a generalized infinite hierarchy of the integrable Riemann-type hydrodynamic equations. A previous Lie symmetry analysis revealed a particular case which was conjectured to be integrable. Namely, a Lie-Baecklund symmetry exists, thus highlighting another associated dynamical system. Here, we investigate these two equations using the gradient-holonomic integrability scheme. Moreover, we construct their infinite hierarchy of conservation laws analytically, using three compatible Poisson structures to prove the complete integrability of both dynamical systems. We investigate these two equations using the so-called gradient-holonomic integrability scheme. Based on this scheme, applied to the equation under consideration, we have analytically constructed its infinite hierarchy of conservation laws, derived two compatible Poisson structures and proved its complete integrability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07900 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On integrability of a new dynamical system associated with the BBM-type hydrodynamic flow Dutykh, Denys Prykarpatskyy, Yarema A. Exactly Solvable and Integrable Systems Mathematical Physics Analysis of PDEs Pattern Formation and Solitons 58J70, 37J35 (primary), 76B15, 35A30, 37K35 (secondary) This article explores the exceptional integrability property of a family of higher-order Benjamin-Bona-Mahony (BBM)-type nonlinear dispersive equations. Here, we highlight its deep relationship with a generalized infinite hierarchy of the integrable Riemann-type hydrodynamic equations. A previous Lie symmetry analysis revealed a particular case which was conjectured to be integrable. Namely, a Lie-Baecklund symmetry exists, thus highlighting another associated dynamical system. Here, we investigate these two equations using the gradient-holonomic integrability scheme. Moreover, we construct their infinite hierarchy of conservation laws analytically, using three compatible Poisson structures to prove the complete integrability of both dynamical systems. We investigate these two equations using the so-called gradient-holonomic integrability scheme. Based on this scheme, applied to the equation under consideration, we have analytically constructed its infinite hierarchy of conservation laws, derived two compatible Poisson structures and proved its complete integrability. |
| title | On integrability of a new dynamical system associated with the BBM-type hydrodynamic flow |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics Analysis of PDEs Pattern Formation and Solitons 58J70, 37J35 (primary), 76B15, 35A30, 37K35 (secondary) |
| url | https://arxiv.org/abs/2407.07900 |