Methods for exact solutions of nonlinear ordinary differential equations\
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912255667339264 |
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| author | Conte, Robert Musette, Micheline Ng, Tuen Wai Wu, Chengfa |
| author_facet | Conte, Robert Musette, Micheline Ng, Tuen Wai Wu, Chengfa |
| contents | In order to find closed form solutions of nonintegrable nonlinear ordinary differential equations, numerous tricks have been proposed. The goal of this short review is to recall classical, 19th-century results, completed in 2006 by Eremenko, which can be turned into algorithms, thus avoiding \textit{ad hoc} assumptions, able to provide \textit{all} (as opposed to some) solutions in a precise class. To illustrate these methods, we present some new such exact solutions, physically relevent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00834 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Methods for exact solutions of nonlinear ordinary differential equations\ Conte, Robert Musette, Micheline Ng, Tuen Wai Wu, Chengfa Exactly Solvable and Integrable Systems Mathematical Physics 33E05, 34Mxx In order to find closed form solutions of nonintegrable nonlinear ordinary differential equations, numerous tricks have been proposed. The goal of this short review is to recall classical, 19th-century results, completed in 2006 by Eremenko, which can be turned into algorithms, thus avoiding \textit{ad hoc} assumptions, able to provide \textit{all} (as opposed to some) solutions in a precise class. To illustrate these methods, we present some new such exact solutions, physically relevent. |
| title | Methods for exact solutions of nonlinear ordinary differential equations\ |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics 33E05, 34Mxx |
| url | https://arxiv.org/abs/2503.00834 |