Geodesic
Classical and nonclassical symmetries for the Krichever–Novikov equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 168 (2011) no. 1, pp. 24-34 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study the Krichever–Novikov equation from the standpoint of the theory of symmetry reductions in partial differential equations. We obtain a Lie group classification. Moreover, we obtain some exact solutions, and we apply the nonclassical method.
Keywords: partial differential equation, symmetry
Mots-clés : exact solution. 
@article{TMF_2011_168_1_a2,
     author = {M. S. Bruz\'on and M. L. Gandarias},
     title = {Classical and nonclassical symmetries for {the~Krichever{\textendash}Novikov} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {24--34},
     year = {2011},
     volume = {168},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_168_1_a2/}
}
TY  - JOUR
AU  - M. S. Bruzón
AU  - M. L. Gandarias
TI  - Classical and nonclassical symmetries for the Krichever–Novikov equation
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2011
SP  - 24
EP  - 34
VL  - 168
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2011_168_1_a2/
LA  - ru
ID  - TMF_2011_168_1_a2
ER  - 
%0 Journal Article
%A M. S. Bruzón
%A M. L. Gandarias
%T Classical and nonclassical symmetries for the Krichever–Novikov equation
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2011
%P 24-34
%V 168
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2011_168_1_a2/
%G ru
%F TMF_2011_168_1_a2
M. S. Bruzón; M. L. Gandarias. Classical and nonclassical symmetries for the Krichever–Novikov equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 168 (2011) no. 1, pp. 24-34. http://geodesic.mathdoc.fr/item/TMF_2011_168_1_a2/

[1] S. I. Svinolupov, V. V. Sokolov, Funkts. analiz i ego pril., 16:4 (1982), 86–87 | DOI | MR | Zbl

[2] R. Hernández Heredero, V. V. Sokolov, S. I. Svinolupov, Physica D, 87:1–4 (1995), 32–36 | DOI | MR | Zbl

[3] V. V. Sokolov, UMN, 43:5(263) (1988), 133–163 | DOI | MR | Zbl

[4] V. E. Adler, Int. Math. Res. Not., 1 (1998), 1–4, arXiv: solv-int/9707015 | DOI | MR | Zbl

[5] I. M. Krichever, S. P. Novikov, UMN, 35:6(216) (1980), 47–68 | DOI | MR | Zbl

[6] S. Igonin, R. Martini, J. Phys. A, 35:46 (2002), 9801–9810, arXiv: nlin/0208006 | DOI | MR | Zbl

[7] N. Euler, M. Euler, J. Nonlin. Math. Phys., 16, Suppl. 1 (2009), 93–106 | DOI | MR

[8] S. I. Svinolupov, V. V. Sokolov, R. I. Yamilov, Dokl. AN SSSR, 271:4 (1983), 802–805, arXiv: nlin/0110027 | MR | Zbl

[9] F. W. Nijhoff, Phys. Lett. A, 297:1–2 (2002), 49–58 | DOI | MR | Zbl

[10] N. Kh. Ibragimov, Gruppy preobrazovanii v matematicheskoi fizike, Nauka, M., 1983 | MR | Zbl

[11] P. Olver, Prilozheniya grupp Li k differentsialnym uravneniyam, Mir, M., 1983 | MR | MR | Zbl

[12] L. V. Ovsyannikov, Gruppovoi analiz differentsialnykh uravnenii, Nauka, M., 1978 | MR | MR | Zbl

[13] G. W. Bluman, J. D. Cole, J. Math. Mech., 18 (1969), 1025–1042 | MR | Zbl

[14] G. W. Bluman, S. Kumei, Symmetries and differential equations, 1989, Springer | DOI | MR | Zbl

[15] M. Abramovits, I. Stigan (red.), Spravochnik po spetsialnym funktsiyam, Nauka, M., 1979 | MR

[16] P. A. Clarkson, Chaos, Solitons and Fractals, 5:12 (1995) | DOI | MR | Zbl

[17] P. A. Clarkson, E. L. Mansfield, SIAM J. Appl. Math., 54:6 (1994), 1693–1719, arXiv: solv-int/9409003 | DOI | MR | Zbl

[18] N. Bilǎ, J. Niesen, J. Symbolic Comput., 38:6 (2004), 1523–1533 | DOI | MR

[19] M. S. Bruzón, M. L. Gandarias, Commun. Nonlinear Sci. Numer. Simul., 13:3 (2008), 517–523 | DOI | MR | Zbl