Integrable Deformations of Algebraic Curves
Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 1, pp. 94-101 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We present a general scheme for determining and studying integrable deformations of algebraic curves, based on the use of Lenard relations. We emphasize the use of several types of dynamical variables: branches, power sums, and potentials.
Keywords: algebraic curves, integrable systems
Mots-clés : Lenard relations.
@article{TMF_2005_144_1_a9,
     author = {Y. Kodama and B. G. Konopelchenko and L. Mart{\'\i}nez Alonso},
     title = {Integrable {Deformations} of {Algebraic} {Curves}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {94--101},
     year = {2005},
     volume = {144},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2005_144_1_a9/}
}
TY  - JOUR
AU  - Y. Kodama
AU  - B. G. Konopelchenko
AU  - L. Martínez Alonso
TI  - Integrable Deformations of Algebraic Curves
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2005
SP  - 94
EP  - 101
VL  - 144
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2005_144_1_a9/
LA  - ru
ID  - TMF_2005_144_1_a9
ER  - 
%0 Journal Article
%A Y. Kodama
%A B. G. Konopelchenko
%A L. Martínez Alonso
%T Integrable Deformations of Algebraic Curves
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2005
%P 94-101
%V 144
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2005_144_1_a9/
%G ru
%F TMF_2005_144_1_a9
Y. Kodama; B. G. Konopelchenko; L. Martínez Alonso. Integrable Deformations of Algebraic Curves. Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 1, pp. 94-101. http://geodesic.mathdoc.fr/item/TMF_2005_144_1_a9/

[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. Enolśki, A. R. Its, V. B. Matveev, Algebro-Geometric Approach to Nonlinear Integrable Equations, Springer, Berlin, 1994; Б. А. Дубровин, С. П. Новиков, УМН, 44:6 (1989), 29–98 ; H. Flaschka, M. G. Forest, D. W. Mclauglin, Commun. Pure Appl. Math., 33 (1980), 739 ; B. A. Dubrovin, Commun. Math. Phys., 145 (1992), 415 | MR | MR | Zbl | DOI | MR | Zbl | DOI | MR

[2] I. M. Krichever, Funkts. analiz i ego prilozh., 22:3 (1988), 37–52 ; 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–L500 ; “Deformations of plane algebraic curves and integrable systems of hydrodynamic type”, Nonlinear Physics: Theory and Experiment II, Proc. Intl. Workshop (Gallipoli, Lecce, Italy, 2002), eds. M. J. Ablowitz et al., World Scientific, River Edge, NJ, 2003, 234 | DOI | MR | Zbl | DOI | Zbl

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

[5] C. L. Siegel, Topics in Complex Function Theory. V. I. Elliptic Functions and Uniformization Theory, Wiley, N.Y., 1969 | MR | Zbl

[6] R. Y. Walker, Algebraic Curves, Springer, Berlin, 1978 | MR | Zbl

[7] S. S. Abhyankar, Algebraic Geometry for Scientists and Engineers, Mathematical Surveys and Monograps, 35, AMS, Providence, RI, 1990 | DOI | MR

[8] B. L. Van der Varden, Algebra, Nauka, M., 1979 | MR | Zbl

[9] L. Redei, Introduction to Algebra, V. 1, Pergamon Press, Oxford, 1967 | MR | Zbl

[10] I. G. Macdonald, Symmetric Functions and Hall Polynomials, Clarendom Press, Oxford, 1979 | MR | Zbl

[11] L. Schwartz, Analyse Mathematique, V. 2, Hermann, Paris, 1967 | MR | Zbl