Electronic Journal of Differential Equations,
Vol. 2001(2001), No. 23, pp. 1-12.
Title: Approximate equivalence transformations and invariant solutions of a
perturbed nonlinear wave equation
Author: R. N. Ibragimov (Univ. of Waterloo, Canada)
Abstract:
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.