T. A. Ivanova, A. D. Popov, “Self-dual Yang–Mills fields in $d=4$ and integrable systems in $1\leq d\leq 3$”, TMF, 102:3 (1995), 384–419; Theoret. and Math. Phys., 102:3 (1995), 280

Teoreticheskaya i Matematicheskaya Fizika

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor
	Guidelines for authors
	License agreement
	Submit a manuscript

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

TMF:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Teoreticheskaya i Matematicheskaya Fizika, 1995, Volume 102, Number 3, Pages 384–419 (Mi tmf1276)

This article is cited in 22 scientific papers (total in 22 papers)

Self-dual Yang–Mills fields in $d=4$ and integrable systems in $1\leq d\leq 3$

T. A. Ivanova, A. D. Popov

Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics

Full-text PDF (3148 kB) Citations (22)

References:

PDF

HTML

Abstract: The Ward correspondence between self-dual Yang–Mills fields and holomorphic vector bundles is used to develop a method for reducing the Lax pair for the self-duality equations of the Yang–Mills model in $d=4$ with respect to the action of continuous symmetry groups. It is well known that reductions of the self-duality equations lead to systems of nonlinear differential equations in dimension $1\leq d\leq 3$. For the integration of the reduced equations, it is necessary to find a Lax pair whose compatibility conditions is these equations. The method makes it possible to obtain systematically a Lax representation for the reduced self-duality equations. This is illustrated by a large number of examples.

Received: 26.06.1994

English version:
Theoretical and Mathematical Physics, 1995, Volume 102, Issue 3, Pages 280–304
DOI: https://doi.org/10.1007/BF01017880

Bibliographic databases:

Language: Russian

Citation: T. A. Ivanova, A. D. Popov, “Self-dual Yang–Mills fields in $d=4$ and integrable systems in $1\leq d\leq 3$”, TMF, 102:3 (1995), 384–419; Theoret. and Math. Phys., 102:3 (1995), 280–304

Citation in format AMSBIB

\Bibitem{IvaPop95}

\by T.~A.~Ivanova, A.~D.~Popov

\paper Self-dual Yang--Mills fields in $d=4$ and integrable systems in~$1\leq d\leq 3$

\jour TMF

\yr 1995

\vol 102

\issue 3

\pages 384--419

\mathnet{http://mi.mathnet.ru/tmf1276}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1348851}

\zmath{https://zbmath.org/?q=an:0854.58046}

\transl

\jour Theoret. and Math. Phys.

\yr 1995

\vol 102

\issue 3

\pages 280--304

\crossref{https://doi.org/10.1007/BF01017880}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995RZ02000008}

Linking options:

https://www.mathnet.ru/eng/tmf1276

https://www.mathnet.ru/eng/tmf/v102/i3/p384

This publication is cited in the following 22 articles:

Sergey V. Bolokhov, Vladimir D. Ivashchuk, “Fluxbrane Polynomials and Melvin-like Solutions for Simple Lie Algebras”, Symmetry, 15:6 (2023), 1199
André Fischer, Olaf Lechtenfeld, “The noncommutative sine-Gordon breather”, Journal of Mathematical Physics, 50:9 (2009)
Olaf Lechtenfeld, Alexander D Popov, “Noncommutative solitons in a supersymmetric chiral model in 2+1 dimensions”, J. High Energy Phys., 2007:06 (2007), 065
Christian Gutschwager, Olaf Lechtenfeld, Tatiana A Ivanova, “Scattering of noncommutative waves and solitons in a supersymmetric chiral model in 2 + 1 dimensions”, J. High Energy Phys., 2007:11 (2007), 052
Masashi Hamanaka, “Non-commutative Ward's conjecture and integrable systems”, Nuclear Physics B, 741:3 (2006), 368
Masashi Hamanaka, “On reductions of noncommutative anti-self-dual Yang–Mills equations”, Physics Letters B, 625:3-4 (2005), 324
Masashi Hamanaka, “Commuting flows and conservation laws for noncommutative Lax hierarchies”, Journal of Mathematical Physics, 46:5 (2005)
Olaf Lechtenfeld, Liuba Mazzanti, Silvia Penati, Alexander D. Popov, Laura Tamassia, “Integrable noncommutative sine-Gordon model”, Nuclear Physics B, 705:3 (2005), 477
Marcus T Grisaru, Liuba Mazzanti, Silvia Penati, Laura Tamassia, “Some properties of the integrable noncommutative sine–Gordon system”, J. High Energy Phys., 2004:04 (2004), 057
Hitoshi Nishino, Subhash Rajpoot, “Noncommutative self-dual supersymmetric Yang–Mills theory”, Physics Letters B, 572:1-2 (2003), 91
Stig Bieling, “Interaction of noncommutative plane waves in (2 $plus$ 1) dimensions”, J. Phys. A: Math. Gen., 35:30 (2002), 6281
M Legar$eacute$, “Reduced systems of (2, 2) pseudo-Euclidean noncommutative self-dual Yang$ndash$Mills theories”, J. Phys. A: Math. Gen., 35:26 (2002), 5489
J.F. Gomes, E.P. Gueuvoghlanian, G.M. Sotkov, A.H. Zimerman, “Electrically charged topological solitons”, Nuclear Physics B, 606:1-2 (2001), 441
Olaf Lechtenfeld, Alexander D. Popov, Bernd Spendig, “Open N=2 strings in a B-field background and noncommutative self-dual Yang–Mills”, Physics Letters B, 507:1-4 (2001), 317
A.V. Shapovalov, A.Yu. Trifonov, “Semiclassical Solutions of the Nonlinear Schrödinger Equation”, JNMP, 6:2 (1999), 127
E.G Floratos, G.K Leontaris, “The Matrix model and the non-commutative geometry of the supermembrane”, Physics Letters B, 464:1-2 (1999), 30
M. Legaré, Lecture Notes in Physics, 502, Supersymmetry and Integrable Models, 1998, 257
M. Legaré, “Lie Superalgebra Valued Self-Dual Yang-Mills Fields and Symmetry Reduction”, JNMP, 4:3-4 (1997), 383
A.D. Popov, C.R. Preitschopf, “Extended conformal symmetries of the self-dual Yang-Mills equations”, Physics Letters B, 374:1-3 (1996), 71
A.D. Popov, M. Bordemann, H. Römer, “Symmetries, currents and conservation laws of self-dual gravity”, Physics Letters B, 385:1-4 (1996), 63

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	512
Full-text PDF :	150
References:	78
First page:	1

Registration to the website

Logotypes