Integrable semiclassical deformations of general algebraic curves and associated conservation laws
Teoretičeskaâ i matematičeskaâ fizika, Tome 151 (2007) no. 3, pp. 458-469 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Based on the Lenard relations, we completely classify integrable deformations of general algebraic curves. We construct the general solution of the Lenard relation from the invariance condition with respect to an element of the Galois group of the curve. We give some examples and also some associated conservation laws.
Keywords: algebraic curve, integrable system, conservation law.
Mots-clés : Lenard relation
@article{TMF_2007_151_3_a11,
     author = {B. G. Konopelchenko and L. Mart{\'\i}nez Alonso and E. Medina},
     title = {Integrable semiclassical deformations of general algebraic curves and associated conservation laws},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {458--469},
     year = {2007},
     volume = {151},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_151_3_a11/}
}
TY  - JOUR
AU  - B. G. Konopelchenko
AU  - L. Martínez Alonso
AU  - E. Medina
TI  - Integrable semiclassical deformations of general algebraic curves and associated conservation laws
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2007
SP  - 458
EP  - 469
VL  - 151
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2007_151_3_a11/
LA  - ru
ID  - TMF_2007_151_3_a11
ER  - 
%0 Journal Article
%A B. G. Konopelchenko
%A L. Martínez Alonso
%A E. Medina
%T Integrable semiclassical deformations of general algebraic curves and associated conservation laws
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2007
%P 458-469
%V 151
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2007_151_3_a11/
%G ru
%F TMF_2007_151_3_a11
B. G. Konopelchenko; L. Martínez Alonso; E. Medina. Integrable semiclassical deformations of general algebraic curves and associated conservation laws. Teoretičeskaâ i matematičeskaâ fizika, Tome 151 (2007) no. 3, pp. 458-469. http://geodesic.mathdoc.fr/item/TMF_2007_151_3_a11/

[1] V. E. Zakharov, S. V. Manakov, S. P. Novikov, L. P. Pitaevskii, Teoriya solitonov. Metod obratnoi zadachi, Nauka, M., 1980 ; E. D. Belokolos, A. I. Bobenko, V. Z. Enol'ski, A. R. Its, V. B. Matveev, Algebro-Geometric approach to nonlinear integrable equations, Springer Ser. Nonlinear Dynamics, Springer, Berlin, 1994 ; Б. А. Дубровин, С. П. Новиков, УМН, 44:6 (1989), 29 ; H. Flaschka, M. G. Forest, D. W. Mclauglin, Commun. Pure Appl. Math., 33 (1980), 739 ; B. A. Dubrovin, Commun. Math. Phys., 145 (1992), 195 | MR | MR | Zbl | Zbl | Zbl | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl

[2] I. M. Krichever, Funkts. analiz i ego prilozh., 22:3 (1988), 37 ; I. M. Krichever, Commun. Pure Appl. Math., 47 (1994), 437 | MR | Zbl | DOI | MR | Zbl

[3] Y. Kodama, B. G. Konopelchenko, J. Phys. A, 35 (2002), L489 | DOI | MR | Zbl

[4] B. G. Konopelchenko, L. Martínez Alonso, J. Phys. A, 37 (2004), 7859 | DOI | MR | Zbl

[5] Yu. Kodama, B. G. Konopelchenko, L. Martines Alonso, TMF, 144 (2005), 94 | DOI | MR | Zbl

[6] Y. Kodama, B. G. Konopelchenko, L. Martínez Alonso, E. Medina, J. Math. Phys., 46 (2005), 113502 | DOI | MR | Zbl

[7] B. G. Konopelchenko, L. Martínez Alonso, E. Medina, J. Phys. A, 39 (2006), 11231 | DOI | MR | Zbl

[8] C. L. Siegel, Topics in complex function theory, v. I. Elliptic Functions and Uniformization Theory, Wiley, New York–London–Sydney, 1969 | MR | Zbl

[9] R. Y. Walker, Algebraic Curves, Springer, New York–Heidelberg–Berlin, 1978 ; S. S. Abhyankar, Algebraic Geometry for Scientists and Engineers, Math. Surveys Monogr., 35, AMS, Providence, RI, 1990 | MR | Zbl | DOI | MR | Zbl

[10] L. Redei, Algebra, v. I, Pergamon, Oxford–New York–Toronto, 1967 | MR | Zbl