Geodesic
Integrable Vector Isotropic Equations Admitting Differential Substitutions of First Order
Matematičeskie zametki, Tome 94 (2013) no. 3, pp. 323-330.

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

A symmetry classification of integrable vector evolution equations of third order admitting Miura-type transformations is presented. We obtain the Bäcklund autotransformation for the new equation as well as differential substitutions relating the solutions of some integrable isotropic equations.
Keywords: integrable vector isotropic equation, symmetry classification of integrable vector evolution equations, Bäcklund autotransformation, differential substitution.
Mots-clés : Miura-type transformation 
@article{MZM_2013_94_3_a0,
     author = {M. Yu. Balakhnev},
     title = {Integrable {Vector} {Isotropic} {Equations} {Admitting} {Differential} {Substitutions} of {First} {Order}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {323--330},
     publisher = {mathdoc},
     volume = {94},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_94_3_a0/}
}
TY  - JOUR
AU  - M. Yu. Balakhnev
TI  - Integrable Vector Isotropic Equations Admitting Differential Substitutions of First Order
JO  - Matematičeskie zametki
PY  - 2013
SP  - 323
EP  - 330
VL  - 94
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2013_94_3_a0/
LA  - ru
ID  - MZM_2013_94_3_a0
ER  - 
%0 Journal Article
%A M. Yu. Balakhnev
%T Integrable Vector Isotropic Equations Admitting Differential Substitutions of First Order
%J Matematičeskie zametki
%D 2013
%P 323-330
%V 94
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2013_94_3_a0/
%G ru
%F MZM_2013_94_3_a0
M. Yu. Balakhnev. Integrable Vector Isotropic Equations Admitting Differential Substitutions of First Order. Matematičeskie zametki, Tome 94 (2013) no. 3, pp. 323-330. http://geodesic.mathdoc.fr/item/MZM_2013_94_3_a0/

[1] A. G. Meshkov, V. V. Sokolov, “Integrable evolution equations on the $N$-dimensional sphere”, Comm. Math. Phys., 232:1 (2002), 1–18 | DOI | MR | Zbl

[2] A. G. Meshkov, V. V. Sokolov, “Klassifikatsiya integriruemykh divergentnykh $N$-komponentnykh evolyutsionnykh sistem”, TMF, 139:2 (2004), 192–208 | DOI | MR | Zbl

[3] A. G. Meshkov, M. Ju. Balakhnev, “Integrable anisotropic evolution equations on a sphre”, SIGMA, 1 (2005), 027, 11 pp. | DOI | MR | Zbl

[4] M. Yu. Balakhnev, “Ob odnom klasse integriruemykh evolyutsionnykh vektornykh uravnenii”, TMF, 142:1 (2005), 13–20 | DOI | MR | Zbl

[5] M. Ju. Balakhnev, A. G. Meshkov, “On a classification of integrable vectorial evolutionary equations”, J. Nonlinear Math. Phys., 15:2 (2008), 212–226 | DOI | MR | Zbl

[6] M. Yu. Balakhnev, A. G. Meshkov, “Integriruemye vektornye evolyutsionnye uravneniya, imeyuschie sokhranyayuschiesya plotnosti nulevogo poryadka”, TMF, 164:2 (2010), 207–213 | DOI | Zbl

[7] M. Yu. Balakhnev, “Differentsialnye podstanovki pervogo poryadka dlya uravnenii integriruemykh v $\mathbb S^n$”, Matem. zametki, 89:2 (2011), 178–189 | DOI | MR | Zbl

[8] H. H. Chen, Y. C. Lee, C. S. Liu, “Integrability of nonlinear hamiltonian systems by inverse scattering method”, Phys. Scr., 20:3-4 (1979), 490–492 | DOI | MR | Zbl

[9] N. Kh. Ibragimov, A. B. Shabat, “O beskonechnykh algebrakh Li–Beklunda”, Funkts. analiz i ego pril., 14:4 (1980), 79–80 | MR | Zbl

[10] V. V. Sokolov, A. B. Shabat, “Classification of integrable evolution equations”, Mathematical Physics Reviews, Vol. 4, Soviet Sci. Rev. Sect. C Math. Phys. Rev., 4, Harwood Academic Publ., Chur, 1984, 221–280 | MR | Zbl

[11] A. V. Mikhailov, A. B. Shabat, V. V. Sokolov, “Simmetriinyi podkhod k klassifikatsii integriruemykh uravnenii”, Integriruemost i kineticheskie uravneniya dlya solitonov, Naukova dumka, Kiev, 1990, 213–279 | MR

[12] A. G. Meshkov, “Necessary conditions of the integrability”, Inverse Problems, 10:3 (1994), 635–653 | DOI | MR | Zbl