Geodesic
Symmetries and soliton solutions of nonlinear equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 63 (1985) no. 1, pp. 50-63 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A new, purely algebraic method is developed for finding soliton solutions of nonlinear equations; it does not require the use of the formalism of the inverse scattering method. As examples, explicit expressions for soliton solutions are constructed for some wellknown equations as well as some not hitherto discussed in the literature. The symmetry basis of the method is associated with infinite-dimensional Lie algebras, these being internal symmetry algebras of the systems considered. 
@article{TMF_1985_63_1_a3,
     author = {A. N. Leznov and V. I. Man'ko and S. M. Chumakov},
     title = {Symmetries and soliton solutions of nonlinear equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {50--63},
     year = {1985},
     volume = {63},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1985_63_1_a3/}
}
TY  - JOUR
AU  - A. N. Leznov
AU  - V. I. Man'ko
AU  - S. M. Chumakov
TI  - Symmetries and soliton solutions of nonlinear equations
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1985
SP  - 50
EP  - 63
VL  - 63
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1985_63_1_a3/
LA  - ru
ID  - TMF_1985_63_1_a3
ER  - 
%0 Journal Article
%A A. N. Leznov
%A V. I. Man'ko
%A S. M. Chumakov
%T Symmetries and soliton solutions of nonlinear equations
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1985
%P 50-63
%V 63
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1985_63_1_a3/
%G ru
%F TMF_1985_63_1_a3
A. N. Leznov; V. I. Man'ko; S. M. Chumakov. Symmetries and soliton solutions of nonlinear equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 63 (1985) no. 1, pp. 50-63. http://geodesic.mathdoc.fr/item/TMF_1985_63_1_a3/

[1] Gardner C. S., Green J. M., Kruskal M. D., Miura R. M., Phys. Rev. Lett., 19:19 (1967), 1095–1097 | DOI

[2] Laks P. D., Matematika, 13, no. 5, Mir, M., 1969, 128–150

[3] Zakharov V. E., Shabat A. B., ZhETF, 61:1 (1971), 118–134 | MR

[4] Zakharov V. E., Shabat A. B., Funkts. analiz i ego prilozh., 8:3 (1974), 43–53 | MR | Zbl

[5] Zakharov V. E., Takhtadzhyan L. A., Faddeev L. D., DAN SSSR, 219:6 (1974), 1334–1337 | MR | Zbl

[6] Faddeev L. D., Itogi nauki i tekhniki, Sovremennye problemy matem., 3, VINITI, M., 1974, 93–180 | MR

[7] Ablowitz M. J., Kaup D. J., Newell A. C., Segur M., Stud. Appl. Math., LIIT (1974), 249–316 | DOI

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

[9] Zakharov V. E., Shabat A. B., Funkts. analiz i ego prilozh., 13:3 (1979), 13–22 | MR | Zbl

[10] Zakharov V. E., Mikhailov A. V., ZhETF, 74:6 (1978), 1953–1979 | MR

[11] Leznov A. N., TMF, 58:1 (1984), 156–160 | MR

[12] Leznov A. N., Proceedings of the Second Conference on Non-Linear Processes in Physics and Turbulence (Kiev, 1983), Gordon and Breach, 1984

[13] Leznov A. N., Man'ko V. I., Chumakov S. M., Soliton solutions for chiral dynamical systems, Preprint No 70, PhIAN USSR, M., 1984

[14] Leznov A. N., Man'ko V. I., Chumakov S. M., Lett. Math. Phys., 8 (1984), 297–303 ; 413–419 | DOI | MR | Zbl | MR | Zbl

[15] Leznov A. N., Smirnov V. G., Shabat A. B., TMF, 51:1 (1982), 10–21 | MR | Zbl

[16] Kats V. G., Izv. AN SSSR, ser. matem., 32 (1968), 1323–1367 | MR | Zbl

[17] Moody R. V., J. Algebra, 10 (1968), 122–230 | DOI | MR

[18] Cherednik I. V., Sovremennye problemy matem., 17, 1981, 175–218 | MR | Zbl