Standard

Bäcklund Transformations and New Integrable Systems on the Plane. / Tsiganov, A. V.

Recent Developments in Integrable Systems and Related Topics of Mathematical Physics - Kezenoi-Am, 2016. ed. / Alexander V. Mikhailov; Victor M. Buchstaber; Sotiris Konstantinou-Rizos. Vol. 273 Springer Nature, 2018. p. 47-74.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

Harvard

Tsiganov, AV 2018, Bäcklund Transformations and New Integrable Systems on the Plane. in AV Mikhailov, VM Buchstaber & S Konstantinou-Rizos (eds), Recent Developments in Integrable Systems and Related Topics of Mathematical Physics - Kezenoi-Am, 2016. vol. 273, Springer Nature, pp. 47-74, International Conference on Mathematical Physics, Kezenoi-Am 2016, Kezenoi-Am, Russian Federation, 31/10/16. https://doi.org/10.1007/978-3-030-04807-5_5

APA

Tsiganov, A. V. (2018). Bäcklund Transformations and New Integrable Systems on the Plane. In A. V. Mikhailov, V. M. Buchstaber, & S. Konstantinou-Rizos (Eds.), Recent Developments in Integrable Systems and Related Topics of Mathematical Physics - Kezenoi-Am, 2016 (Vol. 273, pp. 47-74). Springer Nature. https://doi.org/10.1007/978-3-030-04807-5_5

Vancouver

Tsiganov AV. Bäcklund Transformations and New Integrable Systems on the Plane. In Mikhailov AV, Buchstaber VM, Konstantinou-Rizos S, editors, Recent Developments in Integrable Systems and Related Topics of Mathematical Physics - Kezenoi-Am, 2016. Vol. 273. Springer Nature. 2018. p. 47-74 https://doi.org/10.1007/978-3-030-04807-5_5

Author

Tsiganov, A. V. / Bäcklund Transformations and New Integrable Systems on the Plane. Recent Developments in Integrable Systems and Related Topics of Mathematical Physics - Kezenoi-Am, 2016. editor / Alexander V. Mikhailov ; Victor M. Buchstaber ; Sotiris Konstantinou-Rizos. Vol. 273 Springer Nature, 2018. pp. 47-74

BibTeX

@inproceedings{89cbe2acb2c542d49e88eae5253de113,
title = "B{\"a}cklund Transformations and New Integrable Systems on the Plane",
abstract = "The hyperelliptic curve cryptography is based on the arithmetic in the Jacobian of a curve. In classical mechanics well-known cryptographic algorithms and protocols can be very useful for construct auto-B{\"a}cklund transformations, discretization of continuous flows and study of integrable systems with higher order integrals of motion. We consider application of a standard arithmetic of divisors on genus two hyperelliptic curve for the construction of new auto-B{\"a}cklund transformations for the H{\'e}non-Heiles system. Another type of auto-B{\"a}cklund transformations associated with equivalence relations between unreduced divisors and the construction of the new integrable systems in the framework of the Jacobi method are also discussed.",
keywords = "B{\"a}cklund transformations, Hyperelliptic curve cryptography, Integrable systems",
author = "Tsiganov, {A. V.}",
year = "2018",
month = jan,
day = "1",
doi = "10.1007/978-3-030-04807-5_5",
language = "English",
isbn = "9783030048068",
volume = "273",
pages = "47--74",
editor = "Mikhailov, {Alexander V.} and Buchstaber, {Victor M.} and Sotiris Konstantinou-Rizos",
booktitle = "Recent Developments in Integrable Systems and Related Topics of Mathematical Physics - Kezenoi-Am, 2016",
publisher = "Springer Nature",
address = "Germany",
note = "International Conference on Mathematical Physics, Kezenoi-Am 2016 ; Conference date: 31-10-2016 Through 02-11-2016",

}

RIS

TY - GEN

T1 - Bäcklund Transformations and New Integrable Systems on the Plane

AU - Tsiganov, A. V.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - The hyperelliptic curve cryptography is based on the arithmetic in the Jacobian of a curve. In classical mechanics well-known cryptographic algorithms and protocols can be very useful for construct auto-Bäcklund transformations, discretization of continuous flows and study of integrable systems with higher order integrals of motion. We consider application of a standard arithmetic of divisors on genus two hyperelliptic curve for the construction of new auto-Bäcklund transformations for the Hénon-Heiles system. Another type of auto-Bäcklund transformations associated with equivalence relations between unreduced divisors and the construction of the new integrable systems in the framework of the Jacobi method are also discussed.

AB - The hyperelliptic curve cryptography is based on the arithmetic in the Jacobian of a curve. In classical mechanics well-known cryptographic algorithms and protocols can be very useful for construct auto-Bäcklund transformations, discretization of continuous flows and study of integrable systems with higher order integrals of motion. We consider application of a standard arithmetic of divisors on genus two hyperelliptic curve for the construction of new auto-Bäcklund transformations for the Hénon-Heiles system. Another type of auto-Bäcklund transformations associated with equivalence relations between unreduced divisors and the construction of the new integrable systems in the framework of the Jacobi method are also discussed.

KW - Bäcklund transformations

KW - Hyperelliptic curve cryptography

KW - Integrable systems

UR - http://www.scopus.com/inward/record.url?scp=85059688524&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-04807-5_5

DO - 10.1007/978-3-030-04807-5_5

M3 - Conference contribution

AN - SCOPUS:85059688524

SN - 9783030048068

VL - 273

SP - 47

EP - 74

BT - Recent Developments in Integrable Systems and Related Topics of Mathematical Physics - Kezenoi-Am, 2016

A2 - Mikhailov, Alexander V.

A2 - Buchstaber, Victor M.

A2 - Konstantinou-Rizos, Sotiris

PB - Springer Nature

T2 - International Conference on Mathematical Physics, Kezenoi-Am 2016

Y2 - 31 October 2016 through 2 November 2016

ER -

ID: 37502196