Geodesic
Bдcklund Transformation and Dressing Chains for the Landau–Lifshitz Equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 128 (2001) no. 2, pp. 226-235 
A. B. Borisov. Bдcklund Transformation and Dressing Chains for the Landau–Lifshitz Equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 128 (2001) no. 2, pp. 226-235. http://geodesic.mathdoc.fr/item/TMF_2001_128_2_a5/
@article{TMF_2001_128_2_a5,
     author = {A. B. Borisov},
     title = {B{\cyrd}cklund {Transformation} and {Dressing} {Chains} for the {Landau{\textendash}Lifshitz} {Equation}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {226--235},
     year = {2001},
     volume = {128},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2001_128_2_a5/}
}
TY  - JOUR
AU  - A. B. Borisov
TI  - Bдcklund Transformation and Dressing Chains for the Landau–Lifshitz Equation
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2001
SP  - 226
EP  - 235
VL  - 128
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2001_128_2_a5/
LA  - ru
ID  - TMF_2001_128_2_a5
ER  - 
%0 Journal Article
%A A. B. Borisov
%T Bдcklund Transformation and Dressing Chains for the Landau–Lifshitz Equation
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2001
%P 226-235
%V 128
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2001_128_2_a5/
%G ru
%F TMF_2001_128_2_a5

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

We use the dressing method for the Landau–Lifshitz equation and the breeding procedure to obtain a modified Landau–Lifshitz equation. We find the Darboux transformation (the “dressing”) for the integrable Landau–Lifshitz equation of the anisotropic magnet. We find the Bäcklund transformations and dressing chains.

[1] E. K. Sklyanin, O polnoi integriruemosti uravneniya Landau–Lifshitsa, Preprint E-3-79, LOMI, L., 1979

[2] A. M. Kosevich, B. A. Ivanov, A. S. Kovalev, Nelineinye volny namagnichennosti. Dinamicheskie i topologicheskie solitony, Naukova dumka, Kiev, 1983

[3] A. V. Mikhailov, Phys. Lett. A, 92 (1982), 51 | DOI | MR

[4] Yu. L. Rodin, Lett. Math. Phys., 7 (1983), 3 | DOI | MR | Zbl

[5] A. B. Borisov, FMM, 55 (1983), 230

[6] A. B. Borisov, DAN SSSR, 288 (1986), 1339

[7] A. P. Veselov, A. B. Shabat, Funkts. analiz i ego prilozh., 27 (1993), 3 | MR

[8] E. K. Sklyanin, Funkts. analiz i ego prilozh., 16:4 (1982), 27 | MR | Zbl

[9] A. B. Shabat, R. I. Yamilov, Algebra i analiz, 2:2 (1990), 183 | MR

[10] V. V. Adler, Chastnoe soobschenie, 2000

[11] A. B. Borisov, S. A. Zykov, TMF, 115:2 (1998), 199 | DOI | MR | Zbl

[12] A. V. Mikhailov, A. B. Shabat, V. V. Sokolov, “Simmetriinyi podkhod k klassifikatsii integriruemykh uravnenii”, Integriruemost i kineticheskie uravneniya dlya solitonov, eds. V. G. Baryakhtar, V. E. Zakharov, V. M. Chernousenko, Naukova dumka, Kiev, 1990, 213 | MR

[13] A. V. Mikhailov, A. B. Shabat, Phys. Lett. A, 116:4 (1986), 191 | DOI | MR