Exact solutions of the generalized Lane-Emden equation

Journal of Mathematical Physics

Volumn 41, Issue 10, 2000, Pages 7029-7042

  Goenner, Hubert ^a   Havas, Peter ^b  

^a UNIVERSITY OF GÖTTINGEN   (Germany)

^b Temple University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034345397     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1308076     Document Type: Article

References (69)

1. W. Thomson, Collected Papers (Cambridge University Press, Cambridge, 1911), Vol. 5, p. 266.
2. R. Emden, Gaskugeln (Teubner, Leipzig and Berlin, 1907).
3. R. H. Fowler, Quart. J. pure and appl. Math. 45, 289 (1914); 2 (Oxford Series), 259 (1931), MNRS 91, 63 (1930).
4. R. H. Fowler, Quart. J. pure and appl. Math. 45, 289 (1914); 2 (Oxford Series), 259 (1931), MNRS 91, 63 (1930).
5. R. H. Fowler, Quart. J. pure and appl. Math. 45, 289 (1914); 2 (Oxford Series), 259 (1931), MNRS 91, 63 (1930).
6. G. Sansone, Rend. Maternat, 1, 163 (1940).
7. S. D. Maharaj, P. G. L. Leach, and R. Maartens, Gen. Relativ. Gravit. 23, 261 (1991).
8. G. P. Horedt, Astron. Astrophys. 126, 357 (1986).
9. C. M. Bender et al., J. Math. Phys. 30, 1447 (1989).
10. G. P. Horedt, Astron. Astrophys. 172, 359 (1987).
11. P. M. Lima, J. Comput. Appl. Math. 70, 245 (1996); Appl. Numer. Math. 30, 93 (1999).
12. P. M. Lima, J. Comput. Appl. Math. 70, 245 (1996); Appl. Numer. Math. 30, 93 (1999).
13. I. W. Roxburgh and L. M Stockman, Mon. Not. R. Astron. Soc. 303, 466 (1999).
14. G. Adomian, R. Rach, and N. T. Shawagfeh, Found. Phys. Lett. 8, 161 (1995).
15. N. T Shawagfeh, J. Math. Phys. 34, 4364 (1993).
16. P. B. Burt, Nuovo Cimento Soc. Ital. Fis., B 100, 43 (1987).
17. S. Chandrasekhar, An introduction to the study of stellar structure (Dover, New York, 1957), Chap. IV.
18. H. T. Davis, Introduction to Nonlinear Differential and Integral Equations (Dover, New York, 1962).
19. B. K. Datta, Nuovo Cimento Soc. Ital. Fis., B 111, 1385 (1996).
20. M. H. Wrubel, "Stellar Interiors," in Encyclopedia of Physics, edited by S. Flügge (Springer-Verlag, Berlin 1958), Vol. 51, p. 53.
21. B. Meerson, E. Megged, and T. Tajima, Ap. J. 457, 321 (1996).
22. S. Gnutzmann and U. Ritschel, Z. Phys. B: Condens. Matter 96, 391 (1995).
23. N. A. Bahcall, Ap. J. 186, 1179 (1973).
24. N. A. Bahcall, Ap. J. 198, 249 (1975).
25. L. H. Thomas, Proc. Cambridge Philos. Soc. 13, 542 (1927); E. Fermi, Rend. Acad. Naz. Lincei, Cl. Sci., Fis., Mat., Nat. (6); 6, 602 (1920), E. Hille, J. Analyse Math. 23, 147 (1970).
26. L. H. Thomas, Proc. Cambridge Philos. Soc. 13, 542 (1927); E. Fermi, Rend. Acad. Naz. Lincei, Cl. Sci., Fis., Mat., Nat. (6); 6, 602 (1920), E. Hille, J. Analyse Math. 23, 147 (1970).
27. L. H. Thomas, Proc. Cambridge Philos. Soc. 13, 542 (1927); E. Fermi, Rend. Acad. Naz. Lincei, Cl. Sci., Fis., Mat., Nat. (6); 6, 602 (1920), E. Hille, J. Analyse Math. 23, 147 (1970).
28. L. H. Thomas, Proc. Cambridge Philos. Soc. 13, 542 (1927); E. Fermi, Rend. Acad. Naz. Lincei, Cl. Sci., Fis., Mat., Nat. (6); 6, 602 (1920), E. Hille, J. Analyse Math. 23, 147 (1970).
29. V. Marić and M. Skendžić, Math. Balkanica 3, 312 (1973).
30. E. Hille, Ordinary Differential Equations in the Complex Domain (Wiley, New York, 1976), Sect. 12.4.
31. E. Herlt, Gen. Relativ. Gravit. 28, 919 (1996).
32. P. Havas, Gen. Relativ. Gravit. 24, 599 (1992).
33. K. S. Govinder, P. G. L. Leach, and S. D. Maharaj, Int. J. Theor. Phys. 34, 625 (1995).
34. F. Bavaud, Rev. Mod. Phys. 63, 129 (1991).
35. P. Havas and H. Goenner, Spherically symmetric space-times with constant curvature scalar (unpublished).
36. E. T. Whittaker, Analytical Dynamics, Sec. 48 (4th ed.), New York, 1944.
37. J. D. Logan, Invariant Variational Principles (Academic, New York, 1977).
38. B. A. Huberman and J. P. Crutchfield, Phys. Rev. Lett. 43, 1743 (1979); P. Holmes, Philos. Trans. R. Soc. London, Ser. A 292, 419 (1979).
39. B. A. Huberman and J. P. Crutchfield, Phys. Rev. Lett. 43, 1743 (1979); P. Holmes, Philos. Trans. R. Soc. London, Ser. A 292, 419 (1979).
40. W.-H. Steeb and A. Kunick, Phys. Rev. A 25, 2889 (1982).
41. M. Tabor and J. Weiss, Phys. Rev. A 24, 2157 (1981).
42. F. B. Pelap and T. C. Kofane, Phys. Scr. 57, 410 (1998).
43. E. Lidorikis et al., Physica D 113, 346 (1998).
44. J. M. Dixon and J. A. Tuszynski, Phys. Rev. A 41, 4166 (1990).
45. E. Kamke, Differentialgleichungen, Lösungsmethoden und Lösungen, 7th ed. (Akad. Verlagsgesellschaft, Geest & Portig, Leipzig, 1961).
46. Ph. Rosenau, J. Non-Linear Mechanics 19, 303 (1984).
47. G. P. Horedt, Astron. Astrophys. 160, 148 (1986).
48. James S. Wong, SIAM Rev. 17, 339 (1975).
49. R. C. Flagg, C. D. Luning, and W. L. Perry, J. Comput. Phys. 38, 396 (1980).
50. G. J. Butler and L. H. Erbe, Nonlinear Analysis 11, 207 (1987).
51. P. G. Leach, J. Math. Phys. 26, 2510 (1985).
52. W. Sarlet and L. Y. Bahar, Int. J. Non-Linear Mech. 15, 133 (1980).
53. C. D. Luning and W. L. Perry, J. Math. Phys. 22, 1591 (1981).
54. M. Aripov and DSh. Eshmatov, Sov. Phys. Dokl. 34, 789 (1989).
55. V. R. Gavrilov and V. N. Melnikov, Theor. Math. Phys. 114, 355 (1998).
56. E. N. Glass and G. Szamosi, Phys. Rev. 35, 1205 (1987).
57. E. N. Glass and G. Szamosi, Phys. Rev. 39, 1045 (1989).
58. M. R. Feix and H. R. Lewis, J. Math. Phys. 26, 68 (1985).
59. Ji-Zhong-Xu, Intern. J. Theoret. Phys. 37, 1151 (1998).
60. M. F. Bidaut-Véron and L. Véron, Invent. Math. 106, 489 (1991).
61. L. Cagnon and P. Winternitz, Phys. Lett. A 134, 276 (1989); J. Phys. A 22, 4877 (1989); 22, 4895 (1989).
62. L. Cagnon and P. Winternitz, Phys. Lett. A 134, 276 (1989); J. Phys. A 22, 4877 (1989); 22, 4895 (1989).
63. L. Cagnon and P. Winternitz, Phys. Lett. A 134, 276 (1989); J. Phys. A 22, 4877 (1989); 22, 4895 (1989).
64. P. P. Banerji and G. Cao, J. Phys. A 21, 55 (1989).
65. I. M. Ryshik and I. S. Gradstein, Tables of Series, Products and Integrals (Deutscher Verlag der Wissenschaften, Berlin, 1957).
66. P. F. Byrd and M. D. Friedman, Handbook of Elliptic Integrals for Engineers and Physicists (Springer-Verlag, Berlin 1954).
67. H. Lemke, Sitzungsber. Berliner Math. Gesellsch. 18, 26 (1920); N. N. Bogoljubov und J. A. Mitroposlki, Asymptotische Methoden in der Theorie der nichtlinearen Schwingungen (Akad. Verlagsgesellschaft, Berlin, 1965), p. 6.
68. H. Lemke, Sitzungsber. Berliner Math. Gesellsch. 18, 26 (1920); N. N. Bogoljubov und J. A. Mitroposlki, Asymptotische Methoden in der Theorie der nichtlinearen Schwingungen (Akad. Verlagsgesellschaft, Berlin, 1965), p. 6.
69. G. P. Flessas, in Finite dimensional integrable nonlinear dynamical systems, edited by P. G. L. Leach and W. H. Steeb (World Scientific, Singapore, 1988), pp. 161-173.