Asymptotic solutions of the Landau–Lifshitz equation and quasisteady motion of bubbles in magnetic films

Asymptotic solutions to the system of Landau–Lifshitz and magnetostatic equations corresponding to an isolated bubble in a ferromagnetic film are constructed. The dimensionless small parameter of the asymptotic behavior is $\varepsilon=(2Q)^{-1}$, where $Q$ is the quality factor. Equations that determine the quasisteady dynamics and the structure of bubbles that do not contain Bloeh lines are obtained. The method of constructing single-phase asymptotic solutions of the original equations is based on essentially the same ideas as the Krylov–Bogolyubov method of averaging.