Inverse variational problem for equations in the Riccati chain
| Title: | Inverse variational problem for equations in the Riccati chain |
|---|---|
| Authors: | Sarkar, Pranab, Majhi, Pratik, Panja, Madan Mohan, Talukdar, Benoy |
| Publication Year: | 2024 |
| Collection: | Mathematics Mathematical Physics |
| Subject Terms: | Mathematical Physics, 49.xxx, I.1 |
| More Details: | 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. Comment: 12 pages |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/2406.17529 |
| Accession Number: | edsarx.2406.17529 |
| Database: | arXiv |
| Description not available. |