Exact solutions of the Lane-Emden-type equation

New Astronomy

Volumn 13, Issue 7, 2008, Pages 476-480

  Khalique, C M ^a   Ntsime, P ^a  

^a NORTH WEST UNIVERSITY   (South Africa)

Author keywords

Isothermal gas sphere; Lane Emden equation; Lie group analysis; Noether point symmetries

Indexed keywords

EID: 41749083961     PISSN: 13841076     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.newast.2008.01.002     Document Type: Article

References (48)

1. Adam A.A., and Mahomed F.M. Nonlinear Dyn. 30 (2002) 267
2. Adomian G., Rach R., and Shawagfen N.T. Found. Phys. Lett. 8 (1995) 161
3. Bahcall N.A. ApJ 186 (1973) 1179
4. Bahcall N.A. ApJ 198 (1975) 249
5. Bender C.M., et al. J. Math. Phys. 30 (1989) 1447
6. Bluman G.W., and Kumei S. Symmetries and Differential Equations (1989), Springer Verlag, New York
7. Bozhkov Y., and Martins A.C.G. J. Math. Anal. Appl. 294 (2004) 334
8. Bozhkov Y., and Martins A.C.G. Nonlinear Anal. 57 (2004) 773
9. Burt P.B. NCimB 100 (1987) 43
10. Chandrasekhar S. An Introduction to the Study of Stellar Structure (1957), Dover Publications Inc., New York
11. Datta B.K. NCimB 111 (1996) 1385
12. Davis H.T. Introduction to Nonlinear Differential and Integral Equations (1962), Dover Publications Inc., New York
13. Dresner L. Similarity Solutions of Nonlinear Partial Differential Equations (1983), Pitman Advanced Publishing Program, London
14. Emden R. Gaskugeln Anwendungen der mechanischen Warmen-theorie auf Kosmologie und meteorologische Probleme (1907), Teubner, Leipzig
15. Euler N. J. Nonlinear Math. Phys. 4 (1997) 310
16. Fowler R.H. Quart. J. Math. (Oxford) 45 (1914) 289
17. Fowler R.H. Quart. J. Math. (Oxford) 2 (1931) 259
18. Gnutzmann S., and Ritschel U. Z. Phys. B: Condens. Matter 96 (1995) 391
19. Goenner H. Gen. Relativity Gravitation 33 (2001) 833
20. Goenner H., and Havas P. J. Math. Phys. 41 (2000) 7029
21. Horedt G.P. A&A 126 (1986) 357
22. Horedt G.P. A&A 172 (1987) 359
23. Ibragimov N.H. Elementary Lie Group Analysis and Ordinary Differential Equations (1999), Wiley, Chichester
24. Ibragimov N.H., Kara A.H., and Mahomed F.M. Nonlinear Dyn. 15 (1998) 115
25. Kara A.H., and Mahomed F.M. Int. J. Non-linear Mech. 27 (1992) 919
26. Kara A.H., and Mahomed F.M. Int. J. Non-linear Mech. 28 (1993) 379
27. Kara A.H., Vawda F., and Mahomed F.M. Groups Appl. 1 (1994) 27
28. Khalique, C.M., Mahomed, F.M., Muatjetjeja, B., accepted for publication. J. Nonlinear Math. Phys.
29. Leach P.G.L. J. Math. Phys. 26 (1985) 2510
30. Liao S. Appl. Math. Comput. 142 (2003) 1
31. Lie, S., 1967. Differential Equations, Chelsea, New York (in German).
32. Lima P.M. J. Comput. Appl. Math. 70 (1996) 245
33. Lima P.M. Appl. Num. Math. 30 (1999) 93
34. Mahomed F.M., Kara A.H., and Leach P.G.L. J. Math. Anal. Appl. 178 (1993) 116
35. Meerson E., Megged E., and Tajima T. ApJ 457 (1996) 321
36. Mellin C.M. Int. J. Nonlinear Mech. 29 (1994) 529
37. Momoniat E., and Harley C. NewA 11 (2006) 520
38. Noether, E., 1918. Invariante Variations probleme, König Gesell Wissen Göttingen, Math-Phys Kl, Heft, 2, 235-269.
39. Olver P.J. Applications of Lie Groups to Differential Equations (1993), Springer-Verlag, New York
40. Ovsiannikov L.V. Group Analysis of Differential Equations (1982), Academic Press, New York English translation by WF Ames
41. Roxburgh I.W., and Stockman L.M. MNRAS 303 (1999) 466
42. Sarlet W., and Cantrijn F. SIAM Rev. 23 4 (1981)
43. Shawagfeh N.T. J. Math. Phys. 34 (1993) 4364
44. Thomson W. Collected Papers vol. 5 (1911), Cambridge University Press p. 266
45. Wafo Soh C., and Mahomed F.M. Class. Quantum Grav. 16 (1999) 3553
46. Wazwaz A.M. Appl. Math. Comput. 118 (2001) 287
47. Wong J.S.W. SIAM Rev. 17 (1975) 339
48. Wrubel M.H. Stellar interiors. In: Flugge S. (Ed). Encyclopedia of Physics (1958), Springer-Verlag, Berlin 53