Geodesic
Perturbation of a Simple Wave in a Domain Wall Model
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 1, pp. 91-101 Cet article a éte moissonné depuis la source Math-Net.Ru

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A nonlinear hyperbolic partial differential equation similar to the sine-Gordon equation is considered; it models the dynamics of a domain wall in a weak ferromagnet. If the coefficients are constant, there is a solution in the form of a simple (traveling) wave. In particular cases, it is written in terms of elementary functions. For an equation with variable coefficients, the solutions cannot be written explicitly. In the case of slowly varying coefficients, an asymptotic solution is constructed. The leading order term of the asymptotics represents a simple wave, which is found as a solution to an ordinary nonlinear differential equation with slowly varying coefficients. Different methods for calculating the speed of such a wave are discussed and compared. It is found that the effectiveness of a certain method depends on the ratio between the coefficients of the original equation.
Keywords: simple wave, small parameter, asymptotics.
Mots-clés : perturbation 
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L. A. Kalyakin. Perturbation of a Simple Wave in a Domain Wall Model. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 1, pp. 91-101. http://geodesic.mathdoc.fr/item/TIMM_2023_29_1_a6/

[1] Zvezdin A.K., “Dynamics of domain walls in weak ferromagnets”, Pisma v ZhETF, 29:10 (1979), 605–610

[2] Gareeva Z.V., Chen S.M., “Sverkhbystraya dinamika domennykh granits v antiferromagnetikakh i ferrimagnetikakh s temperaturami kompensatsii magnitnogo i uglovogo momentov (Miniobzor)”, Pisma v ZhETF, 114:4 (2021), 250–262 | DOI | MR

[3] Kanel Ya.I., “O stabilizatsii reshenii zadachi Koshi dlya uravnenii, vstrechayuschikhsya v teorii goreniya”, Mat. sb., 59:101, dopolnitelnyi (1962), 245–288 | MR | Zbl

[4] Uchiyama K., “The behavior of solutions of some non-linear diffusion equations for large time”, J. Math. Kyoto Univ., 18:3 (1978), 453–508 | MR | Zbl

[5] Shapaeva T.B., Murtazin R.R., Ekomasov E.G., “Dinamika domennoi granitsy pod deistviem impulsnogo i gradientnogo magnitnykh polei v redkozemelnykh ortoferritakh”, Izv. RAN. Ser. fizicheskaya, 78:2 (2014), 155–158 | DOI | MR

[6] Maslov V.P., Danilov V.G., Volosov K.A, Matematicheskoe modelirovanie protsessov teplomassoperenosa, Nauka, M., 1987, 352 pp.

[7] Kalyakin L.A., “Vozmuschenie prostoi volny v sisteme s dissipatsiei”, Mat. zametki, 112:4 (2022), 553–566 | DOI | MR | Zbl

[8] Danilov V.G., “Globalnye formuly dlya reshenii kvazilineinykh parabolicheskikh uravnenii s malym parametrom i nekorrektnost”, Mat. zametki, 46:1 (1989), 115–117 | MR | Zbl

[9] Danilov V.G., “Asimptoticheckie resheniya tipa beguschikh voln dlya polulineinykh parabolicheskikh uravnenii s malym parametrom”, Mat. zametki, 48:2 (1990), 148–151 | MR | Zbl