Nonlinear dynamics of the asymmetric chiral field of the \(SU(2)\) group on the semiaxis

Abstract

We study the nonlinear dynamics of a noncollinear semi-bounded ferrimagnet within the framework of the model of the asymmetric chiral field on the \(SU(2)\) group. The boundary conditions corresponding to free spins on the surface of the sample and a homogeneous magnetization distribution in its depth are taken into account. To solve the initial-boundary problem, we propose a special composition of the inverse spectral transform on a torus and the image method. Two classes of particle-like excitations are predicted and analyzed, whose cores are strongly deformed near the boundary of the sample and cause bursts of remagnetization of the surface layers of a ferrimagnet. Far from the surface, they transform into typical solitons of an unbounded medium. We calculate the shifts of the internal oscillation phases and the positions of the soliton centers after their elastic reflection from the boundary of the sample. We obtain analytical solutions that describe the delocalization and destruction of multisolitons in the field of magnetization waves of considerable amplitude, that is, waves that fall on the boundary of the sample and reflect from it. We show that the integrals of motion of a semi-bounded sample for any localized initial perturbation of a ferrimagnet represent sums of independent contributions from strongly nonlinear solitons and quasi-particles of the continuous spectrum of dispersive waves.