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208,926
On Infinitesimal Symmetries of the SelfDual YangMills Equations
, 1998
"... Infinitedimensional algebra of all infinitesimal transformations of solutions of the selfdual YangMills equations is described. It contains as subalgebras the infinitedimensional algebras of hidden symmetries related to gauge and conformal transformations. 1 ..."
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Infinitedimensional algebra of all infinitesimal transformations of solutions of the selfdual YangMills equations is described. It contains as subalgebras the infinitedimensional algebras of hidden symmetries related to gauge and conformal transformations. 1
Selfdual YangMills Equations in Split Signature
, 2009
"... We study the selfdual YangMills equations in split signature. We give a special solution, called the basic split instanton, and describe the ADHM construction in the split signature. Moreover a split version of t’Hooft ansatz is described. 1 ..."
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We study the selfdual YangMills equations in split signature. We give a special solution, called the basic split instanton, and describe the ADHM construction in the split signature. Moreover a split version of t’Hooft ansatz is described. 1
Lie Symmetries of the SelfDual YangMills Equations
, 1997
"... We investigate Lie symmetries of the selfdual YangMills equations in fourdimensional Euclidean space (SDYM). The first prolongation of the symmetry generating vector fields is written down, and its action on SDYM computed. Determining equations are then obtained and solved completely. Lie symmetr ..."
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We investigate Lie symmetries of the selfdual YangMills equations in fourdimensional Euclidean space (SDYM). The first prolongation of the symmetry generating vector fields is written down, and its action on SDYM computed. Determining equations are then obtained and solved completely. Lie
physics/9803028 ON INFINITESIMAL SYMMETRIES OF THE SELFDUAL YANGMILLS EQUATIONS
, 1998
"... An infinitedimensional algebra of all infinitesimal transformations of solutions to the selfdual YangMills equations is described. As subalgebras it contains the infinitedimensional algebras of hidden symmetries related to gauge and conformal transformations. 1 ..."
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An infinitedimensional algebra of all infinitesimal transformations of solutions to the selfdual YangMills equations is described. As subalgebras it contains the infinitedimensional algebras of hidden symmetries related to gauge and conformal transformations. 1
Deformation of surfaces, integrable systems and SelfDual YangMills equation
, 2002
"... We conjecture that many (maybe all) integrable systems and spin systems in 2+1 dimensions can be obtained from the (2+1)dimensional GaussMainardiCodazzi and GaussWeingarten equations, respectively. We also show that the (2+1)dimensional GaussMainardiCodazzi equation which describes the deform ..."
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the deformation (motion) of surfaces is the exact reduction of the YangMillsHiggsBogomolny and SelfDual YangMills equations. On the basis of this observation, we suggest that the (2+1)dimensional GaussMainardiCodazzi equation is a candidate to be integrable and the associated linear problem (Lax
Noncommutative Version of (Anti)SelfDual YangMills Equations
, 2000
"... A noncommutative version of the (anti) selfdual YangMills equations is shown to be related via dimensional reductions to noncommutative formulations of the generalized (SO(3)/SO(2)) nonlinear Schrödinger (NS) equations, of the super Korteweg de Vries (superKdV) as well as of the matrix KdV equ ..."
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A noncommutative version of the (anti) selfdual YangMills equations is shown to be related via dimensional reductions to noncommutative formulations of the generalized (SO(3)/SO(2)) nonlinear Schrödinger (NS) equations, of the super Korteweg de Vries (superKdV) as well as of the matrix Kd
Bäcklund Transformations for Noncommutative AntiSelfDual YangMills Equations
, 709
"... We present Bäcklund transformations for the noncommutative antiselfdual YangMills equation where the gauge group is G = GL(2) and use it to generate a series of exact solutions from a simple seed solution. The solutions generated by this approach are represented in terms of quasideterminants and ..."
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Cited by 5 (1 self)
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We present Bäcklund transformations for the noncommutative antiselfdual YangMills equation where the gauge group is G = GL(2) and use it to generate a series of exact solutions from a simple seed solution. The solutions generated by this approach are represented in terms of quasideterminants
2005b On reductions of noncommutative antiselfdual YangMills equations
 Phys. Lett. B
"... In this paper, we show that various noncommutative integrable equations can be derived from noncommutative antiselfdual YangMills equations in the split signature, which include noncommutative versions of Kortewegde Vries, NonLinear Schrödinger, Nwave, DaveyStewartson and KadomtsevPetviashvi ..."
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Cited by 4 (1 self)
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In this paper, we show that various noncommutative integrable equations can be derived from noncommutative antiselfdual YangMills equations in the split signature, which include noncommutative versions of Kortewegde Vries, NonLinear Schrödinger, Nwave, DaveyStewartson and Kadomtsev
hepth/9702144 On Current Algebra of Symmetries of the SelfDual YangMills Equations
, 1997
"... It is shown that the extended conformal symmetries of the selfdual YangMills equations introduced recently have a simple description in terms of Ward’s twistor construction. 1 ..."
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Cited by 1 (0 self)
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It is shown that the extended conformal symmetries of the selfdual YangMills equations introduced recently have a simple description in terms of Ward’s twistor construction. 1
Bäcklund Transformations and the AtiyahWard Ansatz for Noncommutative AntiSelfDual YangMills Equations
, 2008
"... We present Bäcklund transformations for the noncommutative antiselfdual YangMills equation where the gauge group is G = GL(2) and use it to generate a series of exact solutions from a simple seed solution. The solutions generated by this approach are represented in terms of quasideterminants. We ..."
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Cited by 3 (2 self)
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We present Bäcklund transformations for the noncommutative antiselfdual YangMills equation where the gauge group is G = GL(2) and use it to generate a series of exact solutions from a simple seed solution. The solutions generated by this approach are represented in terms of quasideterminants. We
Results 1  10
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208,926