Geodesic
Numerical realization of the inverse scattering method
Teoretičeskaâ i matematičeskaâ fizika, Tome 83 (1990) no. 3, pp. 323-333 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A method of solving the Cauchy problem for integrable equations that is specially suited to the application of numerical methods is proposed. The dynamics of singular solutions in a differential-difference analog of the nonlinear Schrödinger equation is investigated in detail. 
@article{TMF_1990_83_3_a0,
     author = {I. T. Habibullin and A. G. Shagalov},
     title = {Numerical realization of~the inverse scattering method},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {323--333},
     year = {1990},
     volume = {83},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1990_83_3_a0/}
}
TY  - JOUR
AU  - I. T. Habibullin
AU  - A. G. Shagalov
TI  - Numerical realization of the inverse scattering method
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1990
SP  - 323
EP  - 333
VL  - 83
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1990_83_3_a0/
LA  - ru
ID  - TMF_1990_83_3_a0
ER  - 
%0 Journal Article
%A I. T. Habibullin
%A A. G. Shagalov
%T Numerical realization of the inverse scattering method
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1990
%P 323-333
%V 83
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1990_83_3_a0/
%G ru
%F TMF_1990_83_3_a0
I. T. Habibullin; A. G. Shagalov. Numerical realization of the inverse scattering method. Teoretičeskaâ i matematičeskaâ fizika, Tome 83 (1990) no. 3, pp. 323-333. http://geodesic.mathdoc.fr/item/TMF_1990_83_3_a0/

[1] Zakharov V. E., Manakov S. V., Novikov S. P., Pitaevskii L. P., Teoriya solitonov: Metod obratnoi zadachi, Nauka, M., 1980 | MR

[2] Ablovits M., Sigur Kh., Solitony i metod obratnoi zadachi, Mir, M., 1987 | MR

[3] Vysloukh V. A., Cherednik I. V., DAN SSSR, 289:2 (1986), 336–340 | MR

[4] Ablowitz M. J., Taha T. R., J. Comput. Phys., 55:1 (1984), 192–253 | MR

[5] Arkadev V. A., Pogrebkov A. K., Polivanov M. K., TMF, 53:2 (1982), 163–180 | MR

[6] Arkadev V. A., Pogrebkov A. K., Polivanov M. K., TMF, 54:1 (1983), 23–37 | MR | Zbl

[7] Arkadev V. A., TMF, 58:1 (1984), 38–49 | MR | Zbl

[8] Khabibullin I. T., Zap. nauchn. semin. LOMI, 146, 1983, 137–146 | MR

[9] Shabat A. B., Diff. uravneniya, 15:10 (1979), 1824–1834 | MR | Zbl

[10] Khabibullin I. T., “Diskretnaya approksimatsiya obratnoi zadachi rasseyaniya”, Integriruemye sistemy, BFAN, Ufa, 1982, 68–87

[11] Khabibullin I. T., DAN SSSR, 249:1 (1979), 67–70 | MR

[12] Khabibullin I. T., Shagalov A. G., Zhurn. vychislit. matem. i matem. fiziki, 29:3 (1989), 382–391 | MR

[13] Volkov A. Yu., TMF, 74:1 (1988), 135–139 | MR

[14] Davies B., J. Comput. Phys., 66:1 (1986), 36–49 | DOI | MR | Zbl

[15] Novokshenov V. Yu., Diff. uravneniya, 21:11 (1985), 1915–1926 | MR | Zbl