Symmetry analysis and some exact solutions of cylindrically symmetric null fields in general relativity

Communications in Nonlinear Science and Numerical Simulation

Volumn 16, Issue 11, 2011, Pages 4189-4196

  Gupta, R K ^a   Singh, K ^b  

^a THAPAR UNIVERSITY   (India)

^b JAYPEE UNIVERSITY OF INFORMATION TECHNOLOGY   (India)

Author keywords

Cylindrically symmetric space time; Exact solutions; Symmetry analysis

Indexed keywords

MATHEMATICAL OPERATORS; MATHEMATICAL TRANSFORMATIONS; ORDINARY DIFFERENTIAL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; RELATIVITY;

CYLINDRICALLY SYMMETRIC SPACE-TIME; DIFFERENTIAL OPERATORS; EXACT SOLUTION; FIELD EQUATION; GENERAL RELATIVITY; SPACETIME; SYMMETRIC SPACES; SYMMETRICS; SYMMETRY ANALYSIS; SYMMETRY REDUCTION METHODS;

NONLINEAR EQUATIONS;

EID: 79957901953     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2011.03.006     Document Type: Article

References (19)

1. Rao J.K. Cylindrical symmetric null fields in general relativity. Proc Natn Inst Sci India A 1968, 1(3):367.
2. Stephani H., Kramer D., MacCallum M., Hoenselaers C., Herlt E. Exact solutions of Einstein's field equations 2003, Cambridge University Press, Cambridge, pp-350. Secone ed.
3. Piran T., Safier P.N., Katz J. Cylinderical gravitational waves with two degrees of freedom: an exact solution. Phys Rev D 1986, 34(2):331.
4. Papadopoulos D., Xanthopoulos B.C. Tomimatsu-Sato solutions describe cosmic strings interacting with gravitational waves. Phys Rev D 1990, 41(8):2512.
5. Bluman G.W., Anco S.C. Symmetry and integration methods for differential equations. Appl Math Sci 2002, Springer.
6. Singh K., Gupta R.K. Lie symmetries and exact solutions of a new generalized Hirota-Satsuma coupled KdV system with variable coefficients. Int J Eng Sci 2006, 44(3-4):241.
7. Xiaoda Ji Lie symmetry analysis and some new exact solutions of the WuZhang equation. J Math Phys 2004, 45(1):448.
8. Zhao Li, Fu Jing-Li, Chen Ben-Yong Lie symmetries and conserved quantities for a two-dimensional nonlinear diffusion equation of concentration. Chinese Phys B 2010, 19(1):010301-1.
9. Ma W.X., Chen M. Direct search for exact solutions to the nonlinear Schrödinger equation. Appl Math Comp 2009, 215(8):2835.
10. Bluman G.W., Cole J.D. Similarity methods for differential equations 1974, Springer Verlag, New York.
11. Gandarias M.L., Bruzon M.S. Classical and nonclassical symmetries of a generalized Boussinesq equation. J Nonlinear Math Phys 1998, 5(1):8.
12. Quin S. Nonclassical symmetry reductions for coupled KdV equation. Int J Nonlinear Sci 2006, 2(2):97-103.
13. Bhutani O.P., Singh K. Generalized similarity solutions for the type D fluid in five dimensional flat space. J Math Phys 1998, 39(6):3203.
14. Bhutani O.P., Singh K., Kalra D.K. On certain classes of exact solutions of Einstein equations for rotating fields in conventional and nonconventional form. Int J Eng Sci 2003, 41(7):769.
15. Singh K., Gupta R.K. Exact solutions of a variant Boussinesq system. Int J Eng Sci 2006, 44(18-19):1256.
16. Steinberg S. Symmetry methods in differential equations. Technical Report No. 367, The University of New Mexico, 1979.
17. Ali A.T. New exact solutions of the Einstein vacuum equations for rotating axially symmetric fields. Phys Scr 2009, 79:1.
18. Attallaha S.K., El-Sabbagh M.F., Ali A.T. Isovector fields and similarity solutions of Einstein vacuum equations for rotating fields. Commun Nonlinear Sci Numer Simul 2007, 12:1153.
19. Olver P.J. Application of Lie groups to differential equations in graduate texts in mathematics 1993, vol. 107. Springer, New York.