  Multitime evolution PDEs for Rayleigh waves are considered, using geometrical
ingredients capable to build an ultra-parabolic-hyperbolic differential
operator. Their soliton solutions are found based on appropriate hypotheses and
specific ODEs. These multitime solitons develop complex behavior of deformation
phenomena. The original results include: the form of multitime Rayleigh PDEs,
the construction of multitime Rayleigh solitons via some significant amounts of
analysis and the stability of multitime Rayleigh solitons, which are stable
enough to persist indefinitely. In this context we survey some of the
highlights of multitime PDEs theory, from the more classical single-time case,
to the more recent multitime case, as well as current developments in using
this theory to rigorously prove the sense for several evolution variables and
PDEs.
