By symmetry of the partial differential equation L'\phi'(x')=0 with respect
to the variables replacement x'=x'(x), \phi'=\phi'(\Phi\phi) it is advanced to
understand the compatibility of engaging equations system A\phi'(\Phi\phi)=0,
L\phi(x)=0, where A\phi'(\Phi\phi)=0 is obtained from the initial equation by
replacing the variables, L'=L, \Phi(x) is some weight function. If the equation
A\phi'(\Phi\phi)=0 may be transformed to the form L(\Psi\phi)=0, where \Psi(x)
is the weight function, the symmetry will be named the standard Lie symmetry,
otherwise the generalized symmetry.
It is shown that with the given understanding of the symmetry, D'Alembert
equation for one component field is invariant with respect to any arbitrary
reversible coordinate transformations x'=x'(x). In particular, they contain the
transformations of the conformal and Galilei groups realizing the type of
standard and generalized symmetry for \Phi(x)=\phi'(x'\to x)/\phi(x).