Abstract:
We analyse nonlinear partial di erential equations arising from the modelling
of wave phenomena. A large class of wave equations with dissipation and
source terms are studied using a symmetry approach and the construction of
conservation laws. Some previously unknown conservation laws and symmetries
are obtained. We then proceed to use the multiplier (and homotopy) approach
to construct conservation laws from which we obtain some surprisingly
interesting higher-order variational symmetries. We also nd the corresponding
conserved quantities for a large class of Gordon-type equations similar to
those of the sine-Gordon equation and the relativistic Klein-Gordon equation.
In particular, we direct our research and analysis towards a wave equation
with non-constant coe cient terms, that is, coe cients dependent on time
and space. Finally, we study a class of multi-dimensional wave equations.
