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http://ipicyt.repositorioinstitucional.mx/jspui/handle/1010/2012| Two integrable classes of Emden-Fowler equations with applications in astrophysics and cosmology | |
| Stefan C. Mancas Haret Codratian Rosu | |
| En Embargo | |
| 31-12-2019 | |
| Atribución-NoComercial-SinDerivadas | |
| https://doi.org/10.1515/zna-2018-0062 | |
| Emden–Fowler Equation Painlevé Reduction Parametric Solution Weierstrass Elliptic Function | |
| "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." | |
| Walter de Gruyter GmbH | |
| 2018 | |
| Artículo | |
| Mancas, S. & Rosu, H. (2018). Two Integrable Classes of Emden–Fowler Equations with Applications in Astrophysics and Cosmology. Zeitschrift für Naturforschung A, 73(9), pp. 805-814. doi:10.1515/zna-2018-0062 | |
| FÍSICA | |
| Aparece en las colecciones: | Publicaciones Científicas Nanociencias y Materiales |