Lie group analysis for short pulse equation

Document Type : Original Article


School of Mathematics, Iran University of Science and Technology


In this paper, the classical Lie symmetry analysis and the generalized form of Lie symmetry method are performed for a general short pulse equation. The point, contact and local symmetries for this equation are given. In this paper, we generalize the results of H. Liu and J. Li [2], and add some further facts, such as an optimal system of Lie symmetry subalgebras and two local symmetries.


Main Subjects

[1] G. W. Bluman, A. F. Cheviakov, S. C. Anco, Applications of Symmetry Methods to Partial Differential Equations, Springer, New York, 2010.
[2] H. Liu, J. Li, Lie symmetry analysis and exact solutions for the short pulse equation, Nonlinear Analysis 71 (2009) 2126-2133.
[3] P. J. Olver, Applications of Lie Groups to Differential equations, Second Edition, GTM, Vol. 107, Springer Verlage, New York, 1993.
[4] P. J. Olver, Equivalence, Invariant and Symmetry, Cambridge University Press, Cambridge University Press, Cambridge 1995.
[5] L.V. Ovsiannikov, Group Analysis of Differential Equations, Academic Press, New York, 1982.
[6] E. Parkes, Some periodic and solitary travelling-wave solutions of the short pulse equation, Chaos, Solitons & Fractals, 38 (2008) 154-159.
[7] A. Sakovich, S. Sakovich, Solitary wave solutions of the short pulse equation, J. Phys. A Math. Gen. 39 (2006) L361-L367.
[8] T. Schafer, C. E. Wayne, Propagation of ultra-short optical pulses in cubic nonlinear media, Phys. D 196 (2004) 90-105.