Geodesic
Boundary-value problems on the half-plane for the Ishimori equation that are compatible with the inverse scattering method
Teoretičeskaâ i matematičeskaâ fizika, Tome 91 (1992) no. 3, pp. 363-376 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Examples of boundary conditions compatible with the integrability property of the Ishimori equation are found by adjoining a point symmetry of reflection type to Bficklund and Miura transformations. Soliton solutions of the corresponding boundary-value problems on the half- and quarter-plane are constructed. The interaction of the boundary with the solitons is investigated. 
@article{TMF_1992_91_3_a1,
     author = {I. T. Habibullin},
     title = {Boundary-value problems on the half-plane for the {Ishimori} equation that are compatible with the inverse scattering method},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {363--376},
     year = {1992},
     volume = {91},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1992_91_3_a1/}
}
TY  - JOUR
AU  - I. T. Habibullin
TI  - Boundary-value problems on the half-plane for the Ishimori equation that are compatible with the inverse scattering method
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1992
SP  - 363
EP  - 376
VL  - 91
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1992_91_3_a1/
LA  - ru
ID  - TMF_1992_91_3_a1
ER  - 
%0 Journal Article
%A I. T. Habibullin
%T Boundary-value problems on the half-plane for the Ishimori equation that are compatible with the inverse scattering method
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1992
%P 363-376
%V 91
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1992_91_3_a1/
%G ru
%F TMF_1992_91_3_a1
I. T. Habibullin. Boundary-value problems on the half-plane for the Ishimori equation that are compatible with the inverse scattering method. Teoretičeskaâ i matematičeskaâ fizika, Tome 91 (1992) no. 3, pp. 363-376. http://geodesic.mathdoc.fr/item/TMF_1992_91_3_a1/

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

[2] Fokas A. S., Initial-boundary value problems for a class of nonlinear evolution equations, INS-81-preprint, New York, 1987 ; Physica D, 35 (1989), 167–185 | MR | DOI | Zbl

[3] Sklyanin E. K., Funkts. analiz i ego prilozh., 21:2 (1987), 86–87 | MR | Zbl

[4] Sakhnovich L. A., TMF, 81:1 (1989), 12–23 | MR

[5] Habibullin I. T., “Backlund transformations and integrable initial boundary value problems”, Nonlinear world, v. 1 (Kiev, 1989), World Sci. Publ., 1990, 130–138 | MR | Zbl

[6] Borisov A. B., Phys. Lett. A, 143:1 (1990), 52–56 | DOI | MR

[7] Tarasov V. O., Zap. nauchn. semin. LOMI, 169 (1988), 151–165 | MR | Zbl

[8] Bikbaev R. F., Its A. R., Matem. zametki, 45:5 (1989), 3–9 | MR | Zbl

[9] Khabibullin I. T., TMF, 86:1 (1991), 43–52 | MR | Zbl

[10] Khabibullin I. T., Matem. zametki, 49:4 (1991), 130–137 | MR | Zbl

[11] Khabibullin I. T., Zadachi matematicheskoi fiziki i asimptotiki ikh reshenii, IM BNTs UO AN SSSR, Ufa, 1991

[12] Ishimori J., Progr. Theor. Phys., 72:1 (1984), 33–37 | DOI | MR | Zbl

[13] Boiti M., Konopelchenko B. G., Pempinelli F., Inverse Problems, 1985, no. 1, 33–56 | DOI | MR | Zbl

[14] Arkadjev V. A., Pogrebkov A. K., Polivanov M. G., Physica D, 36 (1989), 189–197 | DOI | MR

[15] Konopelckenko B. G., Matkarimov B. T., J. Math. Phys., 31:11 (1990), 2737–2746 | DOI | MR

[16] Lipovskii V. D., Shirokov A. V., Funkts. analiz i ego prilozh., 23:3 (1989), 65–66 | MR | Zbl