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 and Iosif S. KRASIL'SHCHIK

Edition

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

Other information

Language

English

Type of outcome

Article in a journal

Field of Study

10101 Pure mathematics

Country of publisher

Switzerland

Confidentiality degree

is not subject to a state or trade secret

References:

Annales Henri Poincaré

Impact factor

Impact factor: 1.489

RIV identification code

RIV/47813059:19610/19:A0000046

Organization unit

Mathematical Institute in Opava

DOI

https://doi.org/10.1007/s00023-019-00816-0

UT WoS

000475516100006

EID Scopus

2-s2.0-85068155523

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.

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

Abstract

ORIG CZ

In the original language

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.

Cite

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://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 = {https://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://doi.org/10.1007/s00023-019-00816-0.

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