Geodesic
Symmetries of a certain periodic chain
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Complex Analysis. Mathematical Physics, Tome 162 (2019), pp. 80-84.

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

We consider a periodic closure of a nonlinear integrable two-dimensional three-point chain. Integrability is understood in the sense that the chain admits a wide class of reductions, which are nonlinear hyperbolic Darboux integrable systems with two independent variables. We consider a system obtained as a period-$2$ periodic closure of one of two-dimensional three-point chains found within this framework. For this system, a second-order higher symmetry depending on two arbitrary functions is constructed.
Keywords: two-dimensional integrable chain, periodic chain, symmetry, Darboux integrable system, characteristic Lie ring. 
@article{INTO_2019_162_a7,
     author = {M. N. Poptsova},
     title = {Symmetries of a certain periodic chain},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {80--84},
     publisher = {mathdoc},
     volume = {162},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_162_a7/}
}
TY  - JOUR
AU  - M. N. Poptsova
TI  - Symmetries of a certain periodic chain
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2019
SP  - 80
EP  - 84
VL  - 162
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2019_162_a7/
LA  - ru
ID  - INTO_2019_162_a7
ER  - 
%0 Journal Article
%A M. N. Poptsova
%T Symmetries of a certain periodic chain
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2019
%P 80-84
%V 162
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2019_162_a7/
%G ru
%F INTO_2019_162_a7
M. N. Poptsova. Symmetries of a certain periodic chain. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Complex Analysis. Mathematical Physics, Tome 162 (2019), pp. 80-84. http://geodesic.mathdoc.fr/item/INTO_2019_162_a7/

[1] Adler V. E., Shabat A. B., Yamilov R. I., “Simmetriinyi podkhod k probleme integriruemosti”, Teor. mat. fiz., 125:3 (2000), 355–424 | DOI | MR | Zbl

[2] Zhiber A. V., Murtazina R. D., Khabibullin I. T., Shabat A. B., Kharakteristicheskie koltsa Li i nelineinye integriruemye uravneniya, In-t komp. tekhnologii, M.–Izhevsk, 2012

[3] Ferapontov E. V., “Preobrazovaniya Laplasa sistem gidrodinamicheskogo tipa v invariantakh Rimana”, Teor. mat. fiz., 110:1 (1997), 86–97 | DOI | MR | Zbl

[4] Khabibullin I. T., Poptsova M. N., “Integriruemye dvumernye reshetki. Kharakteristicheskie koltsa Li i ikh klassifikatsiya”, Differentsialnye uravneniya. Matematicheskaya fizika, Itogi nauki i tekhn. Ser. Sovr. mat. prilozh. Temat. obzory, 140, VINITI RAN, M., 2017, 18–29

[5] Khabibullin I. T., Poptsova M. N., “Algebraicheskie svoistva kvazilineinykh dvumerizovannykh tsepochek, svyazannye s integriruemostyu”, Ufim. mat. zh., 10:3 (2018), 89–109

[6] Habibullin I. T., Poptsova M.N., “Classification of a subclass of two-dimensional lattices via characteristic Lie rings”, SIGMA., 13 (2017), 073 | MR | Zbl

[7] Mikhailov A. V., Shabat A. B., Sokolov V. V., “The symmetry approach to classification of integrable equations”, What Is Integrability?, Springer Ser. Nonlin. Dynamics, ed. Zakharov V. E., Springer-Verlag, Berlin–Heidelberg, 1991, 115–184 | DOI | MR | Zbl

[8] Shabat A. B., Yamilov R. I., “To a transformation theory of two-dimensional integrable systems”, Phys. Lett. A., 227:1–2 (1997), 15–23 | DOI | MR | Zbl