  We analyse the complex-valued Klein-Gordon Equation from an integrability
perspective by the implementation of the Lie Theory of Continuous Groups, where
this equation is governed by power-law nonlinearity. We write the equations in
terms of real dependent variables and examine both the two-dimensional and
three-dimensional models. In the case of the two-dimensional model the analysis
is extended by the determination of Noether point symmetries and conserved
vectors via the construction of a Lagrangian.
