Approximate equivalence transformations and invariant solutions of a perturbed nonlinear wav equation

Electronic Journal of Differential Equations

Volumn 2001, Issue , 2001, Pages

  Ibragimo, R N ^a  

^a TEXAS STATE UNIVERSITY   (United States)

Author keywords

Approximate equivalence transformation; Invariant solutions; Lie algebra; Perturbed nonlinear wave equation

Indexed keywords

EID: 52549095077     PISSN: 10726691     EISSN: 10726691     Source Type: Journal    
DOI: None     Document Type: Article

References (12)

1. Ames, W.F., Lohner, R.J., Adams, E., Group properties of uit = [f(u)ux x, Int. J. Nonlin. Mech. 16, 439-447 (1981)
2. Bluman, G.W., Kumei, S., Symmetries and differential equations, SpringerVerlag, New York (1989)
3. Gazizov, R.K., Lecture notes on group classification of differential equations with a small parameter, University of the Witwatersrand and University of North-West, South Africa (1996)
4. Lie, S., On integration of a class of linear partial differential equations by means of definite integrals, Arch. Math VI (3), 1881, 328-368 (in German).
5. Reprinted is S. Lie, Gesammelte Abhandlundgen, Vol. 3, paper XXXV. (English translation published in CRC handbook of Lie Group Analysis of differential equations, Vol. 2, 473-499, Boca Raton, Florida: CRC Press. (1995)
6. Olver, P.J., Application of Lie Group Analysis to differential equations, Springer-Verlag, New York (1993)
7. Oron, A., Rosenau, P., Some symmetries of nonlinear heat and wave equations, Phys. Lett. A, 118 (4), 172-183. (1989)
8. Ovsyannikov, L.V., Group analysis of differential equations, Academic Press, New York (1982)
9. Stephan!, H., Differential equations, Cambridge University Press, Cambridge (1989)
10. Torrisi, M., Valenti, A., Group properties and invariant solutions for infinitesimal transformations of a non-linear Wave Equation, Int. J. Nonlin. Mech. 20, 135-144 (1985)
11. Torrisi, M., Tracina, R., Valenti, A., On equivalence transformations applied to a non-linear Wave Equation, in Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics. Kluwer Academic Publishers, Dordrecht, 367-375 (1993)
12. Torrisi, M., Valenti, A., Preliminary group classification of equation vtt = f(x,vx)vx + g(x,vx), J. Math. Phys. 32 (11) 2988- 2995 (1991)