A nonlinear evolution system of hydrodynamic-type equations describing
a three-dimensional multisublattice magnet is studied. An explicit ex
pression is obtained for the energy density function of magnetic syste
ms whose energy density is invariant to right-and left-spin rotations.
Exact solutions for spin density are obtained in the form of helical
waves for quadratic-biquadratic dependence of the energy density (in t
erms of Cartan's invariant functions) in three-dimensional case. Solut
ions are also obtained for magnon fields inducing such waves. The exis
tence of backward helical waves is predicted. (C) 1998 American Instit
ute of Physics.