Painlevé Analysis, Prelle-Singer Approach, Symmetries and Integrability of Damped Hénon-Heiles System
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866911795865714688 |
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| author | Maheswari, C. Uma Muthuchamy, N. Chandrasekar, V. K. Sahadevan, R. Lakshmanan, M. |
| author_facet | Maheswari, C. Uma Muthuchamy, N. Chandrasekar, V. K. Sahadevan, R. Lakshmanan, M. |
| contents | We consider a modified damped version of Hénon-Heiles system and investigate its integrability. By extending the Painlevé analysis of ordinary differential equations we find that the modified Hénon-Heiles system possesses the Painlevé property for three distinct parametric restrictions. For each of the identified cases, we construct two independent integrals of motion using the well known Prelle-Singer method. We then derive a set of nontrivial non-point symmetries for each of the identified integrable cases of the modified Hénon-Heiles system. We infer that the modified Hénon-Heiles system is integrable for three distinct parametric restrictions. Exact solutions are given explicitly for two integrable cases. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_08410 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Painlevé Analysis, Prelle-Singer Approach, Symmetries and Integrability of Damped Hénon-Heiles System Maheswari, C. Uma Muthuchamy, N. Chandrasekar, V. K. Sahadevan, R. Lakshmanan, M. Exactly Solvable and Integrable Systems Dynamical Systems We consider a modified damped version of Hénon-Heiles system and investigate its integrability. By extending the Painlevé analysis of ordinary differential equations we find that the modified Hénon-Heiles system possesses the Painlevé property for three distinct parametric restrictions. For each of the identified cases, we construct two independent integrals of motion using the well known Prelle-Singer method. We then derive a set of nontrivial non-point symmetries for each of the identified integrable cases of the modified Hénon-Heiles system. We infer that the modified Hénon-Heiles system is integrable for three distinct parametric restrictions. Exact solutions are given explicitly for two integrable cases. |
| title | Painlevé Analysis, Prelle-Singer Approach, Symmetries and Integrability of Damped Hénon-Heiles System |
| topic | Exactly Solvable and Integrable Systems Dynamical Systems |
| url | https://arxiv.org/abs/2403.08410 |