Summary
The continued-fraction conversion method (J. Math. Phys. (N. Y.),29, 1761 (1988)) is used to generate a homologous family of exact solutions to the Lane-Emden equation ϕ(r)″+2ϕ(r)′/r+αϕ(r)p=0, forp=5. An exact solution is also obtained for a generalization of the Lane-Emden equation of the form −ϕ(r)″−2ϕ(r)′/r+αϕ(r)2p+1+λϕ(r)4p+1=0 for arbitrary α, γ andp. A condition is established for the generation of exact solutions from the method.
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References
W. L. Ditto andT. J. Pickett:J. Math. Phys. (N.Y.),29, 1761 (1988).
S. Chandrasekhar:An Introduction to the Study of Stellar Structure (Chicago, Ill., 1939).
P. B. Burt:Quantum Mechanics and Nonlinear Waves (Harwood, New York, N.Y., 1981).
A. N. Khovanskii:The Applications of Continued Fractions (Noordhoff, Groningen, 1963).
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Ditto, W.L., Pickett, T.J. Exact solutions of nonlinear differential equations using continued fractions. Nuov Cim B 105, 429–435 (1990). https://doi.org/10.1007/BF02728824
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DOI: https://doi.org/10.1007/BF02728824