ON NONLINEAR DYNAMICS AND LAWS OF CONSERV ATION IN MAGNETIC MEDIA OF SPONTANEOUSLY BROKEN SYMMETRY

A nonlinear evolution set of differential equations of a hydrodynamic type, which describes three-dimensional multisublattice magnetic is co nsidered. The set is shown to be reduced to a symmetrical t-hyperbolic one and in the local neighbourhood of the initial data variety Cauchy 's problem is correct. The conditions for existence of the hydrodynami cal-type conservation laws are formulated. For a quadratic dependence of the energy functional it is proved that except for the canonical co nservation laws (of energy, spin, momentum densities). there are no ad ditional hydrodynamic integrals. This suggests that the system is not integrated in general (stochastic pattern). A particular case of energ y and flux wave propogation is considered if in the magnetic medium a spontaneous <<magnetization>> vector independent of coordinates and ti me appears, the system describes an anisotropic helical magnetic. For a three-dimensional helical magnetic shock-waves (weak discontinuities ) are predicted and propogation velocities of the weak discontinuities are found. A countable number of differential laws of conservation ar e found for the nonlinear set of differential equations describing the evolution of one-dimensional anisotropic helical magnetic. The soluti ons invariant tinder the Lie-Backlund groups are presented without usi ng a specific form or the exchange integrals.