Geodesic
Asimptotic behaviour of the solution of the Cauchy problem for the Volterra chain with step-like initial data
Teoretičeskaâ i matematičeskaâ fizika, Tome 111 (1997) no. 3, pp. 335-344 
V. L. Vereshchagin. Asimptotic behaviour of the solution of the Cauchy problem for the Volterra chain with step-like initial data. Teoretičeskaâ i matematičeskaâ fizika, Tome 111 (1997) no. 3, pp. 335-344. http://geodesic.mathdoc.fr/item/TMF_1997_111_3_a1/
@article{TMF_1997_111_3_a1,
     author = {V. L. Vereshchagin},
     title = {Asimptotic behaviour of the solution of the {Cauchy} problem for the {Volterra} chain with step-like initial data},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {335--344},
     year = {1997},
     volume = {111},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1997_111_3_a1/}
}
TY  - JOUR
AU  - V. L. Vereshchagin
TI  - Asimptotic behaviour of the solution of the Cauchy problem for the Volterra chain with step-like initial data
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1997
SP  - 335
EP  - 344
VL  - 111
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1997_111_3_a1/
LA  - ru
ID  - TMF_1997_111_3_a1
ER  - 
%0 Journal Article
%A V. L. Vereshchagin
%T Asimptotic behaviour of the solution of the Cauchy problem for the Volterra chain with step-like initial data
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1997
%P 335-344
%V 111
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1997_111_3_a1/
%G ru
%F TMF_1997_111_3_a1

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

The connection between a solution of the Volterra chain tending at infinity to constans and the Riemannian curve of genus one modulated in the sence of Witham is described. The leading term of the asymptotic expansion of the solution is constructed.

[1] S. V. Manakov, ZhETF, 67:8 (1974), 543–555 | MR

[2] A. P. Veselov, TMF, 71:1 (1987), 154–159 | MR

[3] V. L. Vereschagin, Matem. zametki, 44:5 (1988), 584–595 | MR | Zbl

[4] R. F. Bikbaev, Ob uravnenii Kortevega–de Friza s konechnozonnymi granichnymi usloviyami, Preprint BNTs UrO AN SSSR, Ufa, 1988

[5] R. F. Bikbaev, Algebra i analiz, 2:3 (1990), 131–143 | MR

[6] R. F. Bikbaev, TMF, 97:2 (1993), 191–212 | MR | Zbl

[7] V. L. Vereschagin, Nonlinear Analysis, Theory, Methods Applications, 19:2 (1992), 177–185 | DOI | MR | Zbl

[8] V. L. Vereschagin, Matem. zametki, 48:2 (1990), 145–148 | MR | Zbl

[9] V. E. Zakharov, S. V. Manakov, ZhETF, 71:1 (1976), 203–215