Electron. J. Diff. Eqns., Vol. 2001(2001), No. 23, pp. 112.
Approximate equivalence transformations and invariant solutions of a
perturbed nonlinear wave equation
R. N. Ibragimov
Abstract:
We discuss the properties of a perturbed nonlinear wave equation
whose coefficients depend on the firstorder 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 wellknown
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
email: ranis@nbnet.nb.ca 
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