Abstract
A similarity analysis of a nonlinear wave equation in elasticity is studied; in particular, one with anharmonic corrections. The symmetry transformation give rise to exact solutions via the method of invariants. In some cases, graphical figure of the solutions are presented. Furthermore, we consider some cases wherein the velocities of the longitudinal and transversal plane waves are variable. Finally, a brief discussion on how a symmetry analysis on a perturbation of the elasticity equation can be pursued.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Apostol, B.-F.: On a non-linear wave equation in elasticity. Phys. Lett. A 318, 545–552 (2003)
Ozkaya, E., Pakdemirli, M.: Lie group theory and analytical solutions for the axially accelerating string problem. J. Sound Vib. 230, 729–742 (2000)
Bluman, G., Kumei, S.: Symmetries and Differential Equations. Springer-Verlag, New York (1989)
Olver, P.: Applications of Lie Groups to Differential Equations. Springer-Verlag, New York (1986)
Baikov, V.A., Gazizov, R.K., Ibragimov, N.H.: In: Ibragimov, N.H. (ed.) CRC Handbook of Lie Group Analysis of Differential Equations, vol. 3, CRC Press, Boca Raton, FL (1996)
Kara, A.H., Mahomed, F.M., Unal, G.: Approximate symmetries and conservation laws with applications. Int. J. Theor. Phy. 38(9), 2389–2400 (1999)
Alfonito, E., Causo, M.S., Profilo, G., Soliani, G.: A class of nonlinear wave equations containing the continuous Toda case. J. Phy. A 31, 2173–2189 (1998)
Pakdemirli, M., Yurusoy, M., Dolapci, I.T.: Comparison of approximate symmetry methods for differential equations. Acta Applicandae Math. 80(3), 243–271 (2004)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bokhari, A.H., Kara, A.H. & Zaman, F.D. Exact solutions of some general nonlinear wave equations in elasticity. Nonlinear Dyn 48, 49–54 (2007). https://doi.org/10.1007/s11071-006-9050-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-006-9050-z