Potential symmetries

Abstract: We derive and analyze the so-called potential symmetries of certain partial
differential equations. At first we calculate adjoint symmetries to find
integrating factors that provide the conserved currents and flux densities
for the conservation law of the given partial differential equations. For
some partial differential equations one is able to gain a potentialisation
of the given equations by introducing a new dependent variable, the so-
called potential variables. This process can in certain cases be repeated
to obtain a chain of potentialisations for the same starting equation. The
combined auxiliary systems associated to the chain of potentialisations
give, in some cases, interesting higher degree potential symmetries for
PDEs which are realized as Lie point symmetries of the auxiliary systems.