A nonlinear evolution system of hydrodynamic-type equations describing
a three-dimensional multisublattice magnet is investigated. Explicit
form of the energy density function for magnetic systems that have an
invariant energy density relative to right and left spin rotations is
obtained. For quadratic-biquadratic dependence of the energy density (
in terms of Cartan's invariant functions), exact solutions are obtaine
d in the one-dimensional case for spin density in the form of stationa
ry profile waves. Solutions for magnon fields that induce such waves a
re also obtained. (C) 1997 American Institute of Physics.