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The paper studies the dynamic description of non-equilibrium processes in single-sublattice and multisublattice magnets with the spin s=1. In case of magnets with the spin s=1 and SU(3) symmetry of the exchange interaction, there are eight magnetic integrals of motion: the spin and the quadrupole matrix. If there are multiple sublattices, the number of additional magnetic quantities characterizing the state increases to sixteen. The presence of the Casimir invariants makes it possible to reduce the number of independent degrees of freedom. Exchange energy models are presented in terms of Casimir invariants corresponding to SO(3) or SU(3) symmetry groups for all four types of magnetic degrees of freedom. For the homogeneous part of the exchange energy, we have found conditions for the existence of local minima, which correspond to equilibrium values of the magnet. Along with the known waves (quadrupole and Goldstone – for the spin nematic), spectra of collective excitations that take into account ferro-quadrupole excitation, quadro-nematic, quadro- antiferromagnetic, and antiferro-nematic waves excitation, are also obtained. In the case of many-sublattice magnetic systems, we have shown that the selected form of the homogeneous energy model allows us to find possible magnetic orderings and to investigate them for stability.

MODELS OF HAMILTONIAN AND LOW-FREQUENCY SPECTRA OF COLLECTIVE EXCITATIONS IN SPIN S = 1 MAGNETICS