Electron. J. Diff. Eqns., Vol. 2001(2001), No. 23, pp. 1-12.

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

R. N. Ibragimov

We discuss the properties of a perturbed nonlinear wave equation whose coefficients depend on the first-order spatial derivatives. In particular, we obtain a group of transformations which are stable with respect to the given perturbation, and derive the principal Lie algebra and its approximate equivalence transformation. The extension of the principal Lie algebra by one is obtained by means of a well-known classification of low dimensional Lie algebras. We also obtain some invariant solutions and classification of the perturbed equation.

Submitted February 11, 2001. Published April 6, 2001.
Math Subject Classifications: 58J90.
Key Words: Perturbed nonlinear wave equation, Lie algebra, approximate equivalence transformation, invariant solutions.

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Ranis N. Ibragimov
Department of Applied Mathematics
University of Waterloo
Waterloo, ON, N2L 3G1, Canada
e-mail: ranis@nbnet.nb.ca

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