  The theory of nonlinear magnetoacoustic wave in the past has strictly been
focused on purely compressive features of the mode. We show that a complete set
of nonlinear equations necessarily includes both compressional and shear
components of the magnetic field. These two turn out to be described by exactly
the same nonlinear equations, which make the use of such a complete full set of
equations far less complicated than expected. Present results should
considerably enrich the theory of these waves by opening up new frontiers of
investigation and providing some completely new types of nonlinear solutions.
