Transverse spin waves in isotropic ferromagnets
  The comparison of transverse spin wave spectra and its attenuation in Heisenberg ferromagnet and in ferromagnetic Fermi liquid as well in polarized Fermi liquid is undertaken. The transverse spin waves frequency in polarized paramagnetic Fermi liquid as well in a Fermi liquid with spontaneous magnetization is found to be proportional to the square of the wave vector with complex diffusion coefficient such that the damping has a finite value proportional to the scattering rate of quasiparticles at T=0.   This behavior of polarized Fermi liquid contrasts with the behavior of Heisenberg ferromagnet in hydrodynamic regime where the transverse spin wave attenuation appears in terms proportional to the wave vector in fourth power.   The reactive part of diffusion coefficient in paramagnetic state at T=0 proves to be inversely proportional to magnetization whereas in ferromagnetic state it is directly proportional to magnetization. The dissipative part of diffusion coefficient at T=0 in paramagnetic state is polarization independent, whereas in ferromagnetic state it is proportional to square of magnetization. Moreover, the spin wave spectrum in ferromagnetic Fermi liquid proves to be unstable that demonstrates the difficulty of the Fermi liquid description of itinerant ferromagnetism. 
V. P. Mineev