On the symmetries of the modified Emden-type equation
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| Názov: | On the symmetries of the modified Emden-type equation |
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| Autori: | Subhra Mondal, Amitava Choudhuri |
| Zdroj: | Canadian Journal of Physics. 103:993-1000 |
| Publication Status: | Preprint |
| Informácie o vydavateľovi: | Canadian Science Publishing, 2025. |
| Rok vydania: | 2025 |
| Predmety: | 0301 basic medicine, 0303 health sciences, 03 medical and health sciences, Nonlinear Sciences - Exactly Solvable and Integrable Systems, FOS: Physical sciences, Exactly Solvable and Integrable Systems (nlin.SI), 70G65, 70G75, 70H33 |
| Popis: | For an autonomous system, the Lagrangian symmetries are embedded in the symmetries of the differential equation. Recently, it has been found that modified Emden-type equations follow nonstandard Lagrangian functions that involve neither the kinetic energy term nor the potential function. By working with one such Lagrangian, we have calculated the Lagrangian symmetries and explicitly demonstrated that, as in the case of standard Lagrangian functions, the variational symmetries of the nonstandard Lagrangian are also included in the Lie symmetries of the nonlinear differential equation. The Lie algebra is also studied. The Lie symmetry-based solutions to the equation are also derived using invariant curve conditions. |
| Druh dokumentu: | Article |
| Jazyk: | English |
| ISSN: | 1208-6045 0008-4204 |
| DOI: | 10.1139/cjp-2025-0072 |
| DOI: | 10.48550/arxiv.1304.5826 |
| Prístupová URL adresa: | http://arxiv.org/abs/1304.5826 |
| Rights: | CSP TDM arXiv Non-Exclusive Distribution |
| Prístupové číslo: | edsair.doi.dedup.....bac65f3b18fa3e429bd12d9d80bcdcbe |
| Databáza: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | For an autonomous system, the Lagrangian symmetries are embedded in the symmetries of the differential equation. Recently, it has been found that modified Emden-type equations follow nonstandard Lagrangian functions that involve neither the kinetic energy term nor the potential function. By working with one such Lagrangian, we have calculated the Lagrangian symmetries and explicitly demonstrated that, as in the case of standard Lagrangian functions, the variational symmetries of the nonstandard Lagrangian are also included in the Lie symmetries of the nonlinear differential equation. The Lie algebra is also studied. The Lie symmetry-based solutions to the equation are also derived using invariant curve conditions. |
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| ISSN: | 12086045 00084204 |
| DOI: | 10.1139/cjp-2025-0072 |