Geodesic
Perturbation of a Simple Wave in a System with Dissipation
Matematičeskie zametki, Tome 112 (2022) no. 4, pp. 553-566.

Voir la notice de l'article provenant de la source Math-Net.Ru

A differential equation that models the motion of a domain wall is considered. For this equation, in the case of constant coefficients, there exists a solution in the form of a travelling wave which describes the transition from one equilibrium to another. For an equation with slowly varying coefficients, we construct an asymptotic one-phase solution. The phase is found from the Hamilton–Jacobi equation whose coefficients are taken from the asymptotics of the unperturbed wave at infinity. The asymptotic construction is based on the requirement that the first correction is small as compared to the leading term uniformly over a wide range of independent variables.
Keywords: travelling wave, small parameter, asymptotics.
Mots-clés : perturbation 
@article{MZM_2022_112_4_a5,
     author = {L. A. Kalyakin},
     title = {Perturbation of a {Simple} {Wave} in a {System} with {Dissipation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {553--566},
     publisher = {mathdoc},
     volume = {112},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_112_4_a5/}
}
TY  - JOUR
AU  - L. A. Kalyakin
TI  - Perturbation of a Simple Wave in a System with Dissipation
JO  - Matematičeskie zametki
PY  - 2022
SP  - 553
EP  - 566
VL  - 112
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2022_112_4_a5/
LA  - ru
ID  - MZM_2022_112_4_a5
ER  - 
%0 Journal Article
%A L. A. Kalyakin
%T Perturbation of a Simple Wave in a System with Dissipation
%J Matematičeskie zametki
%D 2022
%P 553-566
%V 112
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2022_112_4_a5/
%G ru
%F MZM_2022_112_4_a5
L. A. Kalyakin. Perturbation of a Simple Wave in a System with Dissipation. Matematičeskie zametki, Tome 112 (2022) no. 4, pp. 553-566. http://geodesic.mathdoc.fr/item/MZM_2022_112_4_a5/

[1] A. N. Kolmogorov, I. G. Petrovskii, N. S. Piskunov, “Issledovanie uravneniya diffuzii, soedinennoi s vozrastaniem veschestva, i ego primenenie k odnoi biologicheskoi probleme”, Byulleten MGU. Matem., mekh., 1:6 (1937), 1–25 | Zbl

[2] Dzh. Marri, Nelineinye differentsialnye uravneniya v biologii. Lektsii o modelyakh, Mir, M., 1983

[3] V. P. Maslov, V. G. Danilov, K. A. Volosov, Matematicheskoe modelirovanie protsessov teplomassoperenosa, Nauka, M., 1987 | MR

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

[5] Z. V. Gareeva, S. M. Chen, “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

[6] V. P. Maslov, G. A. Omelyanov, “Asimptoticheskie solitonoobraznye resheniya uravnenii s maloi dispersiei”, UMN, 36:3 (219) (1981), 63–126 | MR | Zbl

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

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

[9] N. N. Bogolyubov, Yu. A. Mitropolskii, Asimptoticheskie metody v teorii nelineinykh kolebanii, Nauka, M., 1974 | MR

[10] M. V. Fedoryuk, Obyknovennye differentsialnye uravneniya, Nauka, M., 1985 | MR

[11] L. A. Kalyakin, “Asymptotics of Dynamical Saddle-node Bifurcations”, Russ. J. Nonlinear Dyn., 18:1 (2022), 119–135 | MR

[12] A. M. Ilin, Soglasovanie asimtoticheskikh razlozhenii reshenii kraevykh zadach, Nauka, M., 1989 | MR