Nonlinear dynamics of the bulk magnetostatic and exhange-dipole modes in the ferromagnetic plate

Abstract: Effective equations of the Davey-Stewartson type are obtained by the multiscale expansion technique, that describe evolution of the three-dimensional magnetostatic excitations in the ferromagnetic plate. The proposed approach admits generalization. It is shown, that in the ferromagnetic plates with thickness more than the exchange length evolution of the three-dimensional exchange-dipole wave packets is also described by the Davey-Stewartson equations. The threshold values of instability of the plane monochromatic waves are calculated. The modulational instability of such waves leads to the formation of coherent structures. The conditions of the formation and explicit solutions for plane soliton excitations are found. In the framework of the proposed model, the possibility of the critical collapse of the space localized two-dimensional wave structures is predicted.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdynamical systemsnumerical analysisexactly solvable and integrable systemsfluid dynamics

Audience: researchers in the topic

Mathematical models and integration methods