The SU(3) symmetry and macroscopic dynamics of magnets with spin s = 1

In the Hamiltonian approach, we derive nonlinear dynamic equations for magnetic media with spin s = 1. We introduce two types of magnetic exchange Hamiltonians corresponding to the Casimir invariants of the SU(3) group. We find the spectra of spin and quadrupole waves corresponding to the states with different symmetries under the time reversal transformation. We consider the effect of dissipative processes and find relaxation fluxes caused by the exchange symmetry of the magnetic Hamiltonian.