Geodesic
Linear pseudopotentials and conservation laws for the Landau–Lifshits equation describing the nonlinear dynamics of a ferromagnet with uniaxial anisotropy
Teoretičeskaâ i matematičeskaâ fizika, Tome 46 (1981) no. 3, pp. 371-381 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The methods of differential geometry are used to obtain a set of pseudopotential representations of the Landau–Lifshits equation that describes the nonlinear dynamics of a uniaxial ferromagnet. It is shown that linear pseudopotentials of a definite type are equivalent to a Lax representation. The direct scattering problem is investigated for some linear spectral problems associated with the Landau–Lifshits equation, and a polynomial series of conservation laws is found. 
@article{TMF_1981_46_3_a10,
     author = {A. E. Borovik and V. N. Robuk},
     title = {Linear pseudopotentials and conservation laws for the {Landau{\textendash}Lifshits} equation describing the nonlinear dynamics of a~ferromagnet with uniaxial anisotropy},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {371--381},
     year = {1981},
     volume = {46},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1981_46_3_a10/}
}
TY  - JOUR
AU  - A. E. Borovik
AU  - V. N. Robuk
TI  - Linear pseudopotentials and conservation laws for the Landau–Lifshits equation describing the nonlinear dynamics of a ferromagnet with uniaxial anisotropy
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1981
SP  - 371
EP  - 381
VL  - 46
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1981_46_3_a10/
LA  - ru
ID  - TMF_1981_46_3_a10
ER  - 
%0 Journal Article
%A A. E. Borovik
%A V. N. Robuk
%T Linear pseudopotentials and conservation laws for the Landau–Lifshits equation describing the nonlinear dynamics of a ferromagnet with uniaxial anisotropy
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1981
%P 371-381
%V 46
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1981_46_3_a10/
%G ru
%F TMF_1981_46_3_a10
A. E. Borovik; V. N. Robuk. Linear pseudopotentials and conservation laws for the Landau–Lifshits equation describing the nonlinear dynamics of a ferromagnet with uniaxial anisotropy. Teoretičeskaâ i matematičeskaâ fizika, Tome 46 (1981) no. 3, pp. 371-381. http://geodesic.mathdoc.fr/item/TMF_1981_46_3_a10/

[1] Landau L. D., Sobranie trudov, t. 1, Nauka, M., 1969, s 128 | MR

[2] Akhiezer I. A., Borovik A. E., “K teorii spinovykh voln konechnoi amplitudy”, ZhETF, 52:2 (1967), 508–513; Ахиезер И. А., Боровик А. Е., “О нелинейных спиновых волнах в ферромагнетиках и антиферромагнетиках”, ЖЭТФ, 52:5 (1967), 1332–1344; Иванов Б. А., Ковалев А. Е., Косевич А. М., ФНТ, 3 (1977), 906

[3] Borovik A. E., Maslov K. V., FNT, 4 (1978), 94

[4] Takhtajan L. A., Phys. Lett., 64A:2 (1977), 235 | DOI | MR

[5] Marchenko V. A., Operatory Shturma-Liuvilya i ikh prilozheniya, Naukova dumka, Kiev, 1978 | MR

[6] Borovik A. E., Pisma ZhETF, 28 (1977), 235

[7] Borovick A. E., Sol. Stat. Comm., 33 (1980)

[8] Wahlquist H. D., Estabrook E. B., “Prolongation structures of nonlinear evolution equations”, J. Math. Phys., 16:1 (1975), 1–7 | DOI | MR | Zbl

[9] Corones J., “Solitons and simple pseudopotentials”, J. Math. Phys., 17:5 (1976), 756–759 | DOI | MR | Zbl

[10] Cartan E., Les systemes differentiles exterieurs, Hermann, Paris, 1945 | MR | Zbl

[11] Zakharov V. E., Faddeev L. D., “Uravnenie Kortevega-de Frisa — vpolne integriruemaya gamiltonova sistema”, Funktsionalnyi analiz i ego prilozh., 5:4 (1971), 18–27 | MR | Zbl

[12] Sklyanin E. K., On complete integrability of the Landau-Lifshitz equation, Preprint LOMI-E-3-79, Leningrad, 1979 | MR