A nonlinear-evolution set of equations of the hydrodynamic type describing a magnet with a noncollinear arrangement of spins is investigated. An explicit expression invariant to right and left spin rotations is used for the energy density. The model under consideration can be enterpreted as a continuum limit of a system of distributed symmetric tops. In the three-dimensional case exact solutions for the spin density are obtained in the form of helical waves for the quadratic-biquadratic energy density (in terms of Cartan's invariant functions). Solutions are also obtained for the magnon fields inducing these waves. The existence of backward helical waves is predicted. Energy transport may occur at an angle greater than pi / 2 relative to the direction of the helical waves. The analytical dependences of the wave vector and of the frequency of the helical wave amplitude, magnetic susceptibility, rigidity, and other constants of the model are found. The predicted property would allow for the construction of backward wave generators based on the use of disordered magnetic materials. The backward electromagnetic waves in a layered disordered magnetodielectric are considered. The relationship between the parameters of electromagnetic waves of the (e) layer and of the (i) layer is obtained.

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