Geodesic
Uniform formulas for the asymptotic solution near the leading front for Maxwell's equations with temporal dispersion and localized initial data
Matematičeskie zametki, Tome 116 (2024) no. 3, pp. 388-395 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Maxwell's equations with temporal dispersion and localized initial data are considered. Using the Maslov canonical operator, we construct a uniform asymptotic solution expressed in terms of the derivative of the Airy function of complicated argument, in the neighborhood of the regular points of the leading wave front.
Keywords: Maxwell's equations, localized initial data, Maslov canonical operator. 
@article{MZM_2024_116_3_a4,
     author = {S. Yu. Dobrokhotov and A. A. Tolchennikov},
     title = {Uniform formulas for the asymptotic solution near the leading front for {Maxwell's} equations with temporal dispersion and localized initial data},
     journal = {Matemati\v{c}eskie zametki},
     pages = {388--395},
     year = {2024},
     volume = {116},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2024_116_3_a4/}
}
TY  - JOUR
AU  - S. Yu. Dobrokhotov
AU  - A. A. Tolchennikov
TI  - Uniform formulas for the asymptotic solution near the leading front for Maxwell's equations with temporal dispersion and localized initial data
JO  - Matematičeskie zametki
PY  - 2024
SP  - 388
EP  - 395
VL  - 116
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MZM_2024_116_3_a4/
LA  - ru
ID  - MZM_2024_116_3_a4
ER  - 
%0 Journal Article
%A S. Yu. Dobrokhotov
%A A. A. Tolchennikov
%T Uniform formulas for the asymptotic solution near the leading front for Maxwell's equations with temporal dispersion and localized initial data
%J Matematičeskie zametki
%D 2024
%P 388-395
%V 116
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_2024_116_3_a4/
%G ru
%F MZM_2024_116_3_a4
S. Yu. Dobrokhotov; A. A. Tolchennikov. Uniform formulas for the asymptotic solution near the leading front for Maxwell's equations with temporal dispersion and localized initial data. Matematičeskie zametki, Tome 116 (2024) no. 3, pp. 388-395. http://geodesic.mathdoc.fr/item/MZM_2024_116_3_a4/

[1] L. D. Landau, E. M. Lifshits, Teoreticheskaya fizika. Elektrodinamika sploshnykh sred, Nauka, 1982 | MR

[2] Yu. A. Kravtsov, Yu. I. Orlov, Geometricheskaya optika neodnorodnykh sred, Nauka, M. | MR

[3] S. Yu. Dobrokhotov, S. A. Sergeev, “Asymptotics of the solution of the Cauchy problem with localized initial conditions for a wave type equation with time dispersion. I. Basic structures”, Russ. J. Math. Phys., 29:2 (2022), 149–169 | DOI | MR

[4] S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Prokolotye lagranzhevy mnogoobraziya i asimptoticheskie resheniya lineinykh uravnenii voln na vode s lokalizovannymi nachalnymi usloviyami”, Matem. zametki, 101:6 (2017), 936–943 | DOI | MR

[5] S. Yu. Dobrokhotov, A. I. Shafarevich, B. Tirozzi, “Localized wave and vortical solutions to linear hyperbolic systems and their application to linear shallow water equations”, Russ. J. Math. Phys., 15:2 (2008), 192–221 | MR

[6] V. P. Maslov, M. V. Fedoryuk, Kvaziklassicheskoe priblizhenie dlya uravnenii kvantovoi mekhaniki, Nauka, M., 1976 | MR

[7] S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. I. Shafarevich, “Novye integralnye predstavleniya kanonicheskogo operatora Maslova v osobykh kartakh”, Izv. RAN. Ser. matem., 81:2 (2017), 53–96 | DOI | MR

[8] S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. A. Tolchennikov, “Uniform formulas for the asymptotic solution of a linear pseudodifferential equation describing water waves generated by a localized source”, Russ. J. Math. Phys., 27:2 (2020), 185–191 | DOI | MR

[9] V. P. Maslov, Teoriya vozmuschenii i asimptoticheskie metody, Izd. MGU, M., 1965 | MR

[10] V. V. Belov, S. Yu. Dobrokhotov, T. Ya. Tudorovskiy, “Operator separation of variables for adiabatic problems in quantum and wave mechanics”, J. Engrg. Math., 55:1–4 (2006), 183–237 | DOI | MR