Integrability of Anti-Self-Dual Vacuum Einstein Equations with
Nonzero Cosmological Constant: An Infinite Hierarchy of
Nonlocal Conservation Laws

J 2019

Integrability of Anti-Self-Dual Vacuum Einstein Equations with Nonzero Cosmological Constant: An Infinite Hierarchy of Nonlocal Conservation Laws

SERGYEYEV, Artur and Iosif S. KRASIL'SHCHIK

Basic information

Original name

Integrability of Anti-Self-Dual Vacuum Einstein Equations with Nonzero Cosmological Constant: An Infinite Hierarchy of Nonlocal Conservation Laws

Authors

SERGYEYEV, Artur (804 Ukraine, guarantor, belonging to the institution) and Iosif S. KRASIL'SHCHIK (643 Russian Federation)

Edition

Annales Henri Poincaré, Cham, Switzerland, Springer International Publishing AG, 2019, 1424-0637

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

Switzerland

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

Annales Henri Poincaré

RIV identification code

RIV/47813059:19610/19:A0000046

Organization unit

Mathematical Institute in Opava

DOI

http://dx.doi.org/10.1007/s00023-019-00816-0

UT WoS

000475516100006

Keywords (in Czech)

Przanowského rovnice; laxovské representace; zákony zachování; kosmologická konstanta; gravitace

Keywords in English

Przanowski equation; Lax representations; conservation laws; cosmological constant; gravity

Links

GBP201/12/G028, research and development project.

Změněno: 20/4/2020 15:58, Mgr. Aleš Ryšavý

Abstract

ORIG CZ

V originále

We present an infinite hierarchy of nonlocal conservation laws for the Przanowski equation, an integrable second-order PDE locally equivalent to anti-self-dual vacuum Einstein equations with nonzero cosmological constant. The hierarchy in question is constructed using a nonisospectral Lax pair for the equation under study. As a by product, we obtain an infinite-dimensional differential covering over the Przanowski equation.

In Czech

Uvádíme nekonečnou hierarchii nelokálních zákonů zachování pro Przanowského rovnici, integrabilní PDR druhého řádu lokálně ekvivalentní s antisamoduálními Einsteinovými rovnicemi ve vakuu s nenulovou kosmologickou konstantou. Zmíněná hierarchie byla získána s využitím neisospektrální laxovské representace pro zkoumanou rovnici. Jako vedlejší důsledek jsme získali nekonečněrozměrné diferenciální nakrytí nad Przanowského rovnicí.

Citovat

SERGYEYEV, Artur and Iosif S. KRASIL'SHCHIK. Integrability of Anti-Self-Dual Vacuum Einstein Equations with Nonzero Cosmological Constant: An Infinite Hierarchy of Nonlocal Conservation Laws. Annales Henri Poincaré. Cham, Switzerland: Springer International Publishing AG, 2019, vol. 20, No 8, p. 2699-2715. ISSN 1424-0637. Available from: https://dx.doi.org/10.1007/s00023-019-00816-0.

@article{32744,
   author = {Sergyeyev, Artur and Krasil'shchik, Iosif S.},
   article_location = {Cham, Switzerland},
   article_number = {8},
   doi = {http://dx.doi.org/10.1007/s00023-019-00816-0},
   keywords = {Przanowski equation; Lax representations; conservation laws; cosmological constant; gravity},
   language = {eng},
   issn = {1424-0637},
   journal = {Annales Henri Poincaré},
   title = {Integrability of Anti-Self-Dual Vacuum Einstein Equations with Nonzero Cosmological Constant: An Infinite Hierarchy of Nonlocal Conservation Laws},
   url = {https://link.springer.com/article/10.1007%2Fs00023-019-00816-0},
   volume = {20},
   year = {2019}
}

TY  - JOUR
ID  - 32744
AU  - Sergyeyev, Artur - Krasil'shchik, Iosif S.
PY  - 2019
TI  - Integrability of Anti-Self-Dual Vacuum Einstein Equations with Nonzero Cosmological Constant: An Infinite Hierarchy of Nonlocal Conservation Laws
JF  - Annales Henri Poincaré
VL  - 20
IS  - 8
SP  - 2699-2715
EP  - 2699-2715
PB  - Springer International Publishing AG
SN  - 14240637
KW  - Przanowski equation
KW  - Lax representations
KW  - conservation laws
KW  - cosmological constant
KW  - gravity
UR  - https://link.springer.com/article/10.1007%2Fs00023-019-00816-0
L2  - https://link.springer.com/article/10.1007%2Fs00023-019-00816-0
N2  - We present an infinite hierarchy of nonlocal conservation laws for the Przanowski equation, an integrable second-order PDE locally equivalent to anti-self-dual vacuum Einstein equations with nonzero cosmological constant. The hierarchy in question is constructed using a nonisospectral Lax pair for the equation under study. As a by product, we obtain an infinite-dimensional differential covering over the Przanowski equation.
ER  -

SERGYEYEV, Artur and Iosif S. KRASIL'SHCHIK. Integrability of Anti-Self-Dual Vacuum Einstein Equations with Nonzero Cosmological Constant: An Infinite Hierarchy of Nonlocal Conservation Laws. \textit{Annales Henri Poincaré}. Cham, Switzerland: Springer International Publishing AG, 2019, vol.~20, No~8, p.~2699-2715. ISSN~1424-0637. Available from: https://dx.doi.org/10.1007/s00023-019-00816-0.

Detailed Information on Publication Record