Nonlinear Schrödinger equations admitted by auto-Bäcklund transformations
Teoretičeskaâ i matematičeskaâ fizika, Tome 100 (1994) no. 2, pp. 199-213 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A generalized formulation of Bäcklund transformations that carry a nonlinear Schrödinger equation into itself is considered, and a class of potentials that satisfy these transformations is found. A set of operators that simplify the analysis of the Lamb equations is introduced.
@article{TMF_1994_100_2_a3,
     author = {R. A. Mishaev and E. Sh. Teplitsky},
     title = {Nonlinear {Schr\"odinger} equations admitted by {auto-B\"acklund} transformations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {199--213},
     year = {1994},
     volume = {100},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1994_100_2_a3/}
}
TY  - JOUR
AU  - R. A. Mishaev
AU  - E. Sh. Teplitsky
TI  - Nonlinear Schrödinger equations admitted by auto-Bäcklund transformations
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1994
SP  - 199
EP  - 213
VL  - 100
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1994_100_2_a3/
LA  - ru
ID  - TMF_1994_100_2_a3
ER  - 
%0 Journal Article
%A R. A. Mishaev
%A E. Sh. Teplitsky
%T Nonlinear Schrödinger equations admitted by auto-Bäcklund transformations
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1994
%P 199-213
%V 100
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1994_100_2_a3/
%G ru
%F TMF_1994_100_2_a3
R. A. Mishaev; E. Sh. Teplitsky. Nonlinear Schrödinger equations admitted by auto-Bäcklund transformations. Teoretičeskaâ i matematičeskaâ fizika, Tome 100 (1994) no. 2, pp. 199-213. http://geodesic.mathdoc.fr/item/TMF_1994_100_2_a3/

[1] Wahlquist H. D., Estabrook F. B., J. Math. Phys., 16 (1975), 1–7 | DOI | MR | Zbl

[2] Wahlquist H. D., Estabrook F. B., J. Math. Phys., 17 (1976), 1293–1297 | DOI | MR | Zbl

[3] Ovsyannikov L. V., Gruppovoi analiz differentsialnykh uravnenii, Nauka, M., 1978 | MR

[4] Ibragimov N. Kh., Gruppy preobrazovanii v matematicheskoi fizike, Nauka, M., 1983 | MR

[5] Gagnon L., Winternitz P., Phys. Rev. A, 39 (1989), 296–306 | DOI | MR

[6] Olver D. J., Applications of Lie groups to differential equations, Springer, N. Y., 1986 | MR

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

[8] Ablowitz M. J., Segur H., Solitons and the inverse scattering transform, SIAM Studies in Applied Mathematics, 4, SIAM, Philadelphia, 1981 | MR | Zbl

[9] Calogero F., Degasperis A., Spectral Transform and solitons: Tools to solve and investigate nonlinear evolution equations, North-Holland Publishing Company, 1982 | MR | Zbl

[10] Khirota R., Solitony, eds. R. Bullaf, P. Kodri, Mir, M., 1980

[11] Lem Dzh.(ml.), Solitony, Mir, M., 1982

[12] Lamb G. L.(jr.), Phys. Lett. A, 48 (1974), 73 | DOI | MR

[13] Lamb G. L.(jr.), J. Math. Phys., 15 (1974), 2157–2165 | DOI | MR

[14] Bullaf R., Kodri P., Solitony, eds. R. Bullaf, P. Kodri, Mir, M., 1980

[15] Harnard J., Winternitz P., J. Math. Phys., 23 (1982), 517–525 | DOI | MR

[16] Kingston J. G., Sophocleous C., J. Math. Phys., 31 (1990), 2597–2602 | DOI | MR | Zbl

[17] Shadwick W. F., J. Math. Phys., 19 (1978), 2312–2317 | DOI | MR | Zbl

[18] Byrnes S. G., J. Math. Phys., 17 (1976), 836–842 | DOI | MR | Zbl

[19] McLaughlin D. W., Scott A., J. Math. Phys., 14 (1973), 1817–1828 | DOI | MR | Zbl