Geodesic
Gauge transformation and generating operators for a quadratic bundle
Teoretičeskaâ i matematičeskaâ fizika, Tome 77 (1988) no. 1, pp. 60-76 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A gauge-covariant formulation of the theory of the generating operator $\Lambda$ for a quadratic bundle is found. On this basis, the method of expansion with respect to “squared solutions” is applied to the auxiliary linear problem $$ \left\{iS_0(x)\frac{d}{dx}+\lambda S_1(x)-\lambda^2\right\}\tilde v(x,\lambda)=0. $$ Thus, for nonlinear evolution equations associated with this problem a hierarchy of Hamiltonian structures is obtained and their complete integrability is proved. Some examples, including equations of Landau–Lifshitz type, are considered for suitable reduction. 
@article{TMF_1988_77_1_a5,
     author = {I. S. Vaklev and M. I. Ivanov},
     title = {Gauge transformation and generating operators for a~quadratic bundle},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {60--76},
     year = {1988},
     volume = {77},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1988_77_1_a5/}
}
TY  - JOUR
AU  - I. S. Vaklev
AU  - M. I. Ivanov
TI  - Gauge transformation and generating operators for a quadratic bundle
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1988
SP  - 60
EP  - 76
VL  - 77
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1988_77_1_a5/
LA  - ru
ID  - TMF_1988_77_1_a5
ER  - 
%0 Journal Article
%A I. S. Vaklev
%A M. I. Ivanov
%T Gauge transformation and generating operators for a quadratic bundle
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1988
%P 60-76
%V 77
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1988_77_1_a5/
%G ru
%F TMF_1988_77_1_a5
I. S. Vaklev; M. I. Ivanov. Gauge transformation and generating operators for a quadratic bundle. Teoretičeskaâ i matematičeskaâ fizika, Tome 77 (1988) no. 1, pp. 60-76. http://geodesic.mathdoc.fr/item/TMF_1988_77_1_a5/

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

[2] Zakharov V. E., Takhtadzhyan L. A., TMF, 38:1 (1979), 26–35 | MR

[3] Gerdjikov V. S., Yanovski A. B., Phys. Lett., 103A:5 (1984), 232 | DOI | MR

[4] Gerdjikov V. S., Yanovski A. B., Commun. Math. Phys., 103 (1986), 549 | DOI | MR | Zbl

[5] Kaup D. J., J. Math. Anal. Appl., 54:3 (1976), 849 ; Kaup D. J., Newell A. C., Adv. Math., 31 (1979), 67 ; Герджиков В. С., Христов Е. Х., Болг. физ. ж., 7:1 (1980), 28 ; 7:2 (1980), 119 | DOI | MR | Zbl | DOI | MR | Zbl | MR | MR

[6] Gerdjikov V. S., Ivanov M. I., Vaklev Y. S., Inverse Problems, 2 (1986), 413 | DOI | MR | Zbl

[7] Gerdzhikov V. S., Ivanov M. I., Bolg. fiz. zh., 10:1 (1983), 13 | MR | Zbl

[8] Gerdzhikov V. S., Ivanov M. I., Kulish P. P., TMF, 44:3 (1980), 342–357 | MR | Zbl

[9] Mikhailov A. V., Physica, 3D:1–2 (1981), 73 | Zbl

[10] Ablovitz M. I., Kaup D. J., Newell A. C., Segur H., Stud. Appl. Math., 53:4 (1974), 249 | DOI | MR

[11] Kaup D. J., Newell A. C., J. Math. Phys., 19:4 (1978), 798 | DOI | MR | Zbl

[12] Kundu A., J. Math. Phys., 25:12 (1984), 3433 | DOI | MR