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.