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Abel’s theorem and Bäcklund transformations for the Hamilton-Jacobi equations. / Tsiganov, A. V.

In: Proceedings of the Steklov Institute of Mathematics, Vol. 295, No. 1, 01.11.2016, p. 243-273.

Research output: Contribution to journal › Article › peer-review

Harvard

Tsiganov, AV 2016, 'Abel’s theorem and Bäcklund transformations for the Hamilton-Jacobi equations', Proceedings of the Steklov Institute of Mathematics, vol. 295, no. 1, pp. 243-273. https://doi.org/10.1134/S0081543816080162

APA

Tsiganov, A. V. (2016). Abel’s theorem and Bäcklund transformations for the Hamilton-Jacobi equations. Proceedings of the Steklov Institute of Mathematics, 295(1), 243-273. https://doi.org/10.1134/S0081543816080162

Vancouver

Tsiganov AV. Abel’s theorem and Bäcklund transformations for the Hamilton-Jacobi equations. Proceedings of the Steklov Institute of Mathematics. 2016 Nov 1;295(1):243-273. https://doi.org/10.1134/S0081543816080162

Author

Tsiganov, A. V. / Abel’s theorem and Bäcklund transformations for the Hamilton-Jacobi equations. In: Proceedings of the Steklov Institute of Mathematics. 2016 ; Vol. 295, No. 1. pp. 243-273.

BibTeX

@article{47bc6b4a8fd344f695a037d42e004c53,
title = "Abel{\textquoteright}s theorem and B{\"a}cklund transformations for the Hamilton-Jacobi equations",
abstract = "We consider an algorithm for constructing auto-B{\"a}cklund transformations for finitedimensional Hamiltonian systems whose integration reduces to the inversion of the Abel map. In this case, using equations of motion, one can construct Abel differential equations and identify the sought B{\"a}cklund transformation with the well-known equivalence relation between the roots of the Abel polynomial. As examples, we construct B{\"a}cklund transformations for the Lagrange top, Kowalevski top, and Goryachev–Chaplygin top, which are related to hyperelliptic curves of genera 1 and 2, as well as for the Goryachev and Dullin–Matveev systems, which are related to trigonal curves in the plane.",
author = "Tsiganov, {A. V.}",
year = "2016",
month = nov,
day = "1",
doi = "10.1134/S0081543816080162",
language = "English",
volume = "295",
pages = "243--273",
journal = "Proceedings of the Steklov Institute of Mathematics",
issn = "0081-5438",
publisher = "МАИК {"}Наука/Интерпериодика{"}",
number = "1",

}

RIS

TY - JOUR

T1 - Abel’s theorem and Bäcklund transformations for the Hamilton-Jacobi equations

AU - Tsiganov, A. V.

PY - 2016/11/1

Y1 - 2016/11/1

N2 - We consider an algorithm for constructing auto-Bäcklund transformations for finitedimensional Hamiltonian systems whose integration reduces to the inversion of the Abel map. In this case, using equations of motion, one can construct Abel differential equations and identify the sought Bäcklund transformation with the well-known equivalence relation between the roots of the Abel polynomial. As examples, we construct Bäcklund transformations for the Lagrange top, Kowalevski top, and Goryachev–Chaplygin top, which are related to hyperelliptic curves of genera 1 and 2, as well as for the Goryachev and Dullin–Matveev systems, which are related to trigonal curves in the plane.

AB - We consider an algorithm for constructing auto-Bäcklund transformations for finitedimensional Hamiltonian systems whose integration reduces to the inversion of the Abel map. In this case, using equations of motion, one can construct Abel differential equations and identify the sought Bäcklund transformation with the well-known equivalence relation between the roots of the Abel polynomial. As examples, we construct Bäcklund transformations for the Lagrange top, Kowalevski top, and Goryachev–Chaplygin top, which are related to hyperelliptic curves of genera 1 and 2, as well as for the Goryachev and Dullin–Matveev systems, which are related to trigonal curves in the plane.

UR - http://www.scopus.com/inward/record.url?scp=85010766134&partnerID=8YFLogxK

U2 - 10.1134/S0081543816080162

DO - 10.1134/S0081543816080162

M3 - Article

AN - SCOPUS:85010766134

VL - 295

SP - 243

EP - 273

JO - Proceedings of the Steklov Institute of Mathematics

JF - Proceedings of the Steklov Institute of Mathematics

SN - 0081-5438

IS - 1

ER -

ID: 8433089