  The extended Einstein-Maxwell-aether-axion model describes internal
interactions inside the system, which contains gravitational, electromagnetic
fields, the dynamic unit vector field describing the velocity of an aether, and
the pseudoscalar field associated with the axionic dark matter. The specific
feature of this model is that the axion field controls the dynamics of the
aether through the guiding functions incorporated into the Jacobson's
constitutive tensor. Depending on the state of the axion field these guiding
functions can control and switch on or switch off the influence of
acceleration, shear, vorticity and expansion of the aether flow on the state of
physical system as a whole. We obtain new exact solutions, which possess the
pp-wave symmetry, and indicate them by the term pp-wave aether modes in
contrast to the pure pp-waves, which can not propagate in this field
conglomerate. These exact solutions describe a specific dynamic state of the
pseudoscalar field, which corresponds to one of the minima of the axion
potential, and switches off the influence of shear and expansion of the aether
flow; the model does not impose restrictions on the Jacobson's coupling
constants and on the axion mass. Properties of these new exact solutions are
discussed.
