Geodesic
Asymptotic solutions of the Landau--Lifshitz equation and quasisteady motion of bubbles in magnetic films
Teoretičeskaâ i matematičeskaâ fizika, Tome 60 (1984) no. 3, pp. 447-467

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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. 
@article{TMF_1984_60_3_a10,
     author = {V. P. Maslov and V. M. Chetverikov},
     title = {Asymptotic solutions of the {Landau--Lifshitz} equation and quasisteady motion of bubbles in magnetic films},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {447--467},
     publisher = {mathdoc},
     volume = {60},
     number = {3},
     year = {1984},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1984_60_3_a10/}
}
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V. P. Maslov; V. M. Chetverikov. Asymptotic solutions of the Landau--Lifshitz equation and quasisteady motion of bubbles in magnetic films. Teoretičeskaâ i matematičeskaâ fizika, Tome 60 (1984) no. 3, pp. 447-467. http://geodesic.mathdoc.fr/item/TMF_1984_60_3_a10/