
Symmetry in Nonlinear Mathematical Physics  2009
Dingjiang Huang (East China University of Science and Technology, China)
Group properties of generalized quasilinear wave equations
Abstract:
Complete group classification of a class of (1+1)dimensional generalized quasilinear wave equations
is performed by using
the LieOvsiannikov method and a compatibility method. Lie reductions of some truly
'variable coefficient' wave equations which are
singled out from the classification results are investigated. As a result,
some classes of exact solutions of these 'variable
coefficient' wave equations are constructed by means of both the reductions
and the additional equivalent transformations. Furthermore,
The nonclassical symmetry to the generalized quasilinear wave equation
is also studied exhaustively. This enabled to obtain new exact
solutions, describing the evolution of various wave patterns.

