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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.17529 |
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| _version_ | 1866929399458168832 |
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| author | Sarkar, Pranab Majhi, Pratik Panja, Madan Mohan Talukdar, Benoy |
| author_facet | Sarkar, Pranab Majhi, Pratik Panja, Madan Mohan Talukdar, Benoy |
| contents | The nonstandard Lagrangian representations of Ricatti and Riccati-type equations that exist in the literature cannot be obtained using Helmholtz solution of the inverse problem. In this work we consider Riccati and higher-order Riccati equations and construct their standard Lagrangian representation by using a simple variant of the Helmholtz theory. We make use of the self-adjoint form of the linear equations corresponding to odd-order equations in the Riccati chain to provide a symmetry-based approach for the solution of inverse problem. Explicit results presented for Lagrangians of the first and third-order Riccati equations show that one cannot Hamiltonize the Riccati family of equations by the traditional method used in classical mechanics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17529 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inverse variational problem for equations in the Riccati chain Sarkar, Pranab Majhi, Pratik Panja, Madan Mohan Talukdar, Benoy Mathematical Physics 49.xxx I.1 The nonstandard Lagrangian representations of Ricatti and Riccati-type equations that exist in the literature cannot be obtained using Helmholtz solution of the inverse problem. In this work we consider Riccati and higher-order Riccati equations and construct their standard Lagrangian representation by using a simple variant of the Helmholtz theory. We make use of the self-adjoint form of the linear equations corresponding to odd-order equations in the Riccati chain to provide a symmetry-based approach for the solution of inverse problem. Explicit results presented for Lagrangians of the first and third-order Riccati equations show that one cannot Hamiltonize the Riccati family of equations by the traditional method used in classical mechanics. |
| title | Inverse variational problem for equations in the Riccati chain |
| topic | Mathematical Physics 49.xxx I.1 |
| url | https://arxiv.org/abs/2406.17529 |