Geodesic
Asymptotic behaviour of the solution of the two-dimensional Dirac system with rapidly oscillating coefficients
Sbornik. Mathematics, Tome 190 (1999) no. 2, pp. 233-254 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An asymptotic expansion is constructed and substantiated for the solution of the boundary-value problem for the two-dimensional elliptic system of Dirac equations with rapidly oscillating coefficients, which holds uniformly with respect to the complex variable and the two real variables. 
@article{SM_1999_190_2_a3,
     author = {O. M. Kiselev},
     title = {Asymptotic behaviour of the solution of the two-dimensional {Dirac} system with rapidly oscillating coefficients},
     journal = {Sbornik. Mathematics},
     pages = {233--254},
     year = {1999},
     volume = {190},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1999_190_2_a3/}
}
TY  - JOUR
AU  - O. M. Kiselev
TI  - Asymptotic behaviour of the solution of the two-dimensional Dirac system with rapidly oscillating coefficients
JO  - Sbornik. Mathematics
PY  - 1999
SP  - 233
EP  - 254
VL  - 190
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1999_190_2_a3/
LA  - en
ID  - SM_1999_190_2_a3
ER  - 
%0 Journal Article
%A O. M. Kiselev
%T Asymptotic behaviour of the solution of the two-dimensional Dirac system with rapidly oscillating coefficients
%J Sbornik. Mathematics
%D 1999
%P 233-254
%V 190
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1999_190_2_a3/
%G en
%F SM_1999_190_2_a3
O. M. Kiselev. Asymptotic behaviour of the solution of the two-dimensional Dirac system with rapidly oscillating coefficients. Sbornik. Mathematics, Tome 190 (1999) no. 2, pp. 233-254. http://geodesic.mathdoc.fr/item/SM_1999_190_2_a3/

[1] Zakharov V. E., Shabat A. B., “Skhema integrirovaniya nelineinykh evolyutsionnykh uravnenii matematicheskoi fiziki metodom obratnoi zadachi rasseyaniya, I”, Funkts. analiz i ego prilozh., 8:3 (1974), 43–53 | MR | Zbl

[2] Dryuma V. S., “Ob analiticheskom reshenii dvumernogo uravneniya Kortevega–de Vriza”, Pisma v ZhETF, 19 (1974), 753–757

[3] Ablowitz M. J., Bar Yaacov D., Fokas A. S., “On the inverse scattering transform for the Kadomtsev–Petviashvili equation”, Stud. Appl. Math., 69 (1983), 135–143 | MR | Zbl

[4] Fokas A. S., Ablowitz M. J., “On the inverse scattering transform of multidimensional nonlinear equations related to first-order systems in the plane”, J. Math. Phys., 25:8 (1984), 2494–2505 | DOI | MR | Zbl

[5] Vekua N. I., Obobschennye analiticheskie funktsii, Nauka, M., 1959

[6] Novikov R. G., Khenkin G. M., “$\overline\partial$-uravnenie v mnogomernoi zadache rasseyaniya”, UMN, 42:3 (1987), 93–152 | MR | Zbl

[7] Lipovskii V. D., “Gamiltonova struktura uravneniya KP-II v klasse ubyvayuschikh dannykh Koshi”, Funkts. analiz i ego prilozh., 20:4 (1986), 35–45 | MR | Zbl

[8] Krichever I. M., “Spektralnaya teoriya dvumernykh periodicheskikh operatorov i ee prilozheniya”, UMN, 44:2 (1989), 121–184 | MR | Zbl

[9] Fokas A. S., Sung L. J., “On the solvalability on the $N$-wave, Davey–Stewartson and Kadomtsev–Petviashvili equations”, Inverse Problems, 8 (1992), 673–708 | DOI | MR | Zbl

[10] Buslaev V. S., “Kvaziklassicheskoe priblizhenie dlya uravnenii s periodicheskimi koeffitsientami”, UMN, 42:6 (1987), 77–98 | MR | Zbl

[11] Dobrokhotov S. Yu., “Rezonansy v asimptotike resheniya zadachi Koshi dlya uravneniya Shredingera s bystroostsilliruyuschim konechnozonnym potentsialom”, Matem. zametki, 44:3 (1988), 319–340 | MR | Zbl

[12] Dubrovin B. A., Matveev V. B., Novikov S. P., “Nelineinye uravneniya tipa Kortevega–de Friza, konechnozonnye lineinye operatory i abelevy mnogoobraziya”, UMN, 31:1 (1976), 55–136 | MR | Zbl

[13] Kiselev O. M., “Asimptotika bessolitonnogo resheniya uravneniya Devi–Styuartsona, II”, Differents. uravneniya, 33:6 (1997), 812–819 | MR | Zbl

[14] Shabat B. V., Vvedenie v kompleksnyi analiz, Chast I, Nauka, M., 1985 | MR

[15] Olver F., Asimptotika i spetsialnye funktsii, Nauka, M., 1990 | MR | Zbl

[16] Maslov V. P., Teoriya vozmuschenii i asimptoticheskie metody, Nauka, M., 1965

[17] Babich V. M., Buldyrev V. S., Asimptoticheskie metody v zadachakh difraktsii korotkikh voln, Nauka, M., 1972 | MR

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

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

[20] Fedoryuk M. V., Asimptotika. Integraly i ryady, Nauka, M., 1987 | MR

[21] Arnold V. I., Varchenko A. N., Gusein-Zade S. M., Osobennosti differentsiruemykh otobrazhenii. Monodromiya i asimptotiki integralov, Nauka, M., 1984 | MR

[22] Kiselev O. M., “Asimptotika mnogomernogo integrala Koshi s bystro ostsilliruyuschei eksponentoi”, Matem. zametki, 58:2 (1995), 231–242 | MR | Zbl