Non-linear dynamics and two-dimensional solitons for spin \( S=1\) ferromagnets with biquadratic exchange

We develop a consistent semiclassical theory of spin dynamics for an isotropic ferromagnet with a spin \( S=1\) taking into consideration both bilinear and biquadratic over spin operators exchange interaction. For such non-Heisenberg magnets, a peculiar class of spin oscillations and waves, for which the quantum spin expectation value \( {\rm {\bf m}}=\) does not change it direction, but changes in length, is presented. Such ``longitudinal'' excitations do not exist in regular magnets, dynamics of which are described in terms of the Landau-Lifshitz equation or by means of the spin Heisenberg Hamiltonian. We demonstrate the presence of non-linear uniform oscillations and waves, as well as self-localized dynamical excitations (solitons) with finite energy. A possibility of excitation of such oscillations by ultrafast laser pulse is discussed.