Geodesic
To the question of large-amplitude electron oscillations in a plasma slab
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 3, pp. 456-469 
E. V. Chizhonkov. To the question of large-amplitude electron oscillations in a plasma slab. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 3, pp. 456-469. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_3_a4/
@article{ZVMMF_2011_51_3_a4,
     author = {E. V. Chizhonkov},
     title = {To the question of large-amplitude electron oscillations in a~plasma slab},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {456--469},
     year = {2011},
     volume = {51},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_3_a4/}
}
TY  - JOUR
AU  - E. V. Chizhonkov
TI  - To the question of large-amplitude electron oscillations in a plasma slab
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2011
SP  - 456
EP  - 469
VL  - 51
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_3_a4/
LA  - ru
ID  - ZVMMF_2011_51_3_a4
ER  - 
%0 Journal Article
%A E. V. Chizhonkov
%T To the question of large-amplitude electron oscillations in a plasma slab
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2011
%P 456-469
%V 51
%N 3
%U http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_3_a4/
%G ru
%F ZVMMF_2011_51_3_a4

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

A new approach is proposed for constructing and analyzing piecewise smooth exact solutions of the system of quasilinear hyperbolic equations that models the simplest electron oscillations in a plasma slab. A necessary and sufficient condition for their existence and uniqueness is established. An approximate numerical–analytical solution method is constructed for smooth initial data.

[1] Akhiezer A. I., Lyubarskii G. Ya., “K nelineinoi teorii kolebanii elektronnoi plazmy”, Dokl. AN SSSR, 80:2 (1951), 193–195 | Zbl

[2] Rowlands G., Brodin G., Stenflo L., “Exact analytic solutions for nonlinear waves in cold plasmas”, J. Plasma Phys., 74:4 (2008), 569–573 | DOI

[3] Albritton J., Koch P., “Cold plasma wavebreaking: propagating of energetic electrones”, Phys. Fluids, 18 (1975), 1136–1139 | DOI

[4] Gorbunov L. M., Frolov A. A., Chizhonkov E. V., Andreev N. E., “Oprokidyvanie nelineinykh tsilindricheskikh kolebanii plazmy”, Fiz. plazmy, 36:4 (2010), 375–386 | MR

[5] Rozhdestvenskii B. L., Yanenko N. N., Sistemy kvazilineinykh uravnenii i ikh prilozheniya k gazovoi dinamike, Nauka, M., 1968 | MR

[6] Kulikovskii A. G., Pogorelov N. V., Semenov A. Yu., Matematicheskie voprosy chislennogo resheniya giperbolicheskikh sistem uravnenii, Fizmatlit, M., 2001 | MR

[7] Chizhonkov E. V., “Chislennoe modelirovanie aksialnykh reshenii nekotorykh nelineinykh zadach”, Vychisl. metody i programmirovaniya, 11 (2010), 215–227

[8] Chandrasekhar S., Ellipsoidal figures of equilibrium, Yale Univ. Press, New Haven, 1969 | Zbl

[9] Amiranashvili Sh., Yu M. Y., Stenflo L., Brodin G., Servin M., “Nonlinear standing waves in bounded plasmas”, Phys. Rev., 66 (2002), 046403, 6 pp. | MR

[10] Esarey E., Sprangle P., Krall J., Ting A., “Overview of plasma-based acceleration concepts”, IEEE Trans. Plasma Sci., 24 (1996), 252 | DOI

[11] Mora P., Antonsen T. M., “Kinetic modelling of intense, short laser pulses propagating in tenuous plasmas”, Phys. Plasmas, 4 (1997), 217–229 | DOI | MR

[12] Goriely A., Hyde C., “Necessary and sufficient conditions for finite time singularities in ordinary differential equations”, J. Differential Equat., 161 (2000), 422–448 | DOI | MR | Zbl

[13] Kamke E., Spravochnik po obyknovennym differentsialnym uravneniyam, Nauka, M., 1965 | MR

[14] Arnold V. I., Obyknovennye differentsialnye uravneniya, Nauka, M., 1971 | MR

[15] Koddington E. L., Levinson N., Teoriya obyknovennykh differentsialnykh uravnenii, Izd-vo inostr. lit., M., 1958

[16] Bakhvalov N. S., Zhidkov N. P., Kobelkov G. M., Chislennye metody, Izd. 6-e, BINOM. Laboratoriya znanii, M., 2008

[17] Aliev Yu. M., Stenflo L., “Large-amplitude electron oscillations in a plasma slab”, Phys. Scripta, 50 (1994), 701–702 | DOI

[18] Dawson J. M., “Nonlinear electron oscillations in a cold plazma”, Phys. Rev., 113:2 (1959), 383–387 | DOI | MR | Zbl

[19] Zeldovich Ya. B., Myshkis A. D., Elementy matematicheskoi fiziki, Nauka, M., 1973 | MR

[20] Gelfand I. M., Zueva N. M., Imshennik V. S. i dr., “K teorii nelineinykh kolebanii elektronnoi plazmy”, Zh. vychisl. matem. i matem. fiz., 7:2 (1967), 322–347