Two integrable classes of Emden-Fowler equations with applications in astrophysics and cosmology
"We show that some Emden–Fowler (EF) equations encountered in astrophysics and cosmology belong to two EF integrable classes of the type d2z/dχ2=Aχ−λ−2zn for λ=(n−1)/2 (class 1), and λ=n+1 (class 2). We find their corresponding invariants which reduce them to first-order nonlinear ordinary diff...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2018 |
| País: | México |
| Institución: | Instituto Potosino de Investigación Científica y Tecnológica |
| Repositorio: | Repositorio Institucional del IPICYT |
| OAI Identifier: | oai:ipicyt.repositorioinstitucional.mx:1010/2012 |
| Acceso en línea: | http://ipicyt.repositorioinstitucional.mx/jspui/handle/1010/2012 |
| Access Level: | acceso embargado |
| Palabra clave: | info:eu-repo/classification/Autor/Emden–Fowler Equation info:eu-repo/classification/Autor/Painlevé info:eu-repo/classification/Autor/Reduction info:eu-repo/classification/Autor/Parametric Solution info:eu-repo/classification/Autor/Weierstrass Elliptic Function info:eu-repo/classification/cti/1 info:eu-repo/classification/cti/22 |
| Sumario: | "We show that some Emden–Fowler (EF) equations encountered in astrophysics and cosmology belong to two EF integrable classes of the type d2z/dχ2=Aχ−λ−2zn for λ=(n−1)/2 (class 1), and λ=n+1 (class 2). We find their corresponding invariants which reduce them to first-order nonlinear ordinary differential equations. Using particular solutions of such EF equations, the two classes are set in the autonomous nonlinear oscillator the form d2ν/dt2+adν/dt+b(ν−νn)=0, where the coefficients a, b depend only on λ,n. For both classes, we write closed-form solutions in parametric form. The illustrative examples from astrophysics and general relativity correspond to two n = 2 cases from class 1 and 2, and one n = 5 case from class 1, all of them yielding Weierstrass elliptic solutions. It is also noticed that when n = 2, the EF equations can be studied using the Painlevé reduction method, since they are a particular case of equations of the type d2z/dχ2=F(χ)z2 , where F(χ) is the Kustaanheimo-Qvist function." |
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