The spectra of the coupled magnetoelastic waves of an easy-plane ferromagnet with a negative biquadratic interaction are investigated. It is shown that in this case the existence region of the quadrupolar phase is narrowed substantially in comparison with the case of a positive biquadratic interaction. The phase diagram of the system is constructed.

Possible types of phase transitions as well as the spectra of coupled magnetoelastic waves are studied in an easy-plane ferromagnet with a rigidly fixed face. It is shown that the presence of such mechanical boundary conditions leads to a change in the type of phase transition. The dynamic properties of the system become most interesting at the point of absolute instability of the system rather than at the phase transition point.

The phase states and spectra of coupled magnetoelastic waves of a non-Heisenberg ferromagnet with complex single-ion anisotropy are investigated. The influence of inclined anisotropy on the phase states and spectra of the system is determined. The phase diagrams of the system are constructed for different relationships among the material constants.

The phase states and the spectra of elementary excitations of a ferromagnet with a biquadratic exchange interaction and a spin-2 magnetic ion are investigated. The phase diagrams of the system are constructed for different relationships among the material constants. It is shown that the phase diagram is substantially altered at large values of the single-ion anisotropy constants and biquadratic exchange constant.

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