The Global Dynamics of the Painlevé-Gambier Equations XVIII, XXI, and XXII
In this paper, we describe the global dynamics of the Painlevé-Gambier equations numbered XVIII: (Formula presented.), XXI: (Formula presented.), and XXII: (Formula presented.). We obtain three rational functions as their first integrals and classify their phase portraits in the Poincaré disc. The m...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:310302 |
| Acceso en línea: | https://ddd.uab.cat/record/310302 https://dx.doi.org/urn:doi:10.3390/math13050756 |
| Access Level: | acceso abierto |
| Palabra clave: | Painlevé-Gambier equations Phase portrait Poincaré disc First integral |
| Sumario: | In this paper, we describe the global dynamics of the Painlevé-Gambier equations numbered XVIII: (Formula presented.), XXI: (Formula presented.), and XXII: (Formula presented.). We obtain three rational functions as their first integrals and classify their phase portraits in the Poincaré disc. The main reason for considering these three Painlevé-Gambier equations is due to the paper of Guha, P., et al., where the authors studied these three differential equations in order to illustrate a method to generate nonlocal constants of motion for a special class of nonlinear differential equations. Here, we want to complete their studies describing all of the dynamics of these equations. This demonstrates that the phase portraits of equations XVIII and XXI in the Poincaré disc are topologically equivalent. |
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