#### DMCA

## 2005b On reductions of noncommutative anti-self-dual Yang-Mills equations

Venue: | Phys. Lett. B |

Citations: | 4 - 1 self |

### Citations

122 |
Komaba lectures on noncommutative solitons and D-branes
- Harvey
(Show Context)
Citation Context ...ed intensively for the last several years. NC gauge theories are equivalent to ordinary gauge theories in the presence of background magnetic fields and succeeded in revealing various aspects of them =-=[1]-=-. NC solitons especially play important roles in the study of D-brane dynamics, such as the confirmation of Sen’s conjecture on tachyon condensation [2]. One of the distinguished features of NC theori... |

32 |
Exact noncommutative KP and KdV multi-solitons
- Paniak
- 2001
(Show Context)
Citation Context ... to a NC reduced ASDYM equation: ( −α ′ − 3uy 0 4˙u − u ′′′ + 3u ′ ⋆ u + 3u ⋆ u ′ + αy + [u, α]⋆ − α ′ ) = 0. (4.13) − 3uy Hence we get α = −3∂ −1 x uy := −3 ∫ x uy(x ′ )dx ′ , and the NC KP equation =-=[6, 17]-=-: ( u ′′′ − 3 (u ′ ⋆ u + u ⋆ u ′ ) − 3∂ −1 x uyy − 3[u, ∂ −1 ) x uy]⋆ . (4.14) ˙u = 1 4 If we neglect y-dependence, the present discussion gives rise to another reduction to NC KdV equation from ASDYM... |

30 |
KP or mKP: Noncommutative mathematics of Lagrangian
- Kupershmidt
- 2000
(Show Context)
Citation Context ... to a NC reduced ASDYM equation: ( −α ′ − 3uy 0 4˙u − u ′′′ + 3u ′ ⋆ u + 3u ⋆ u ′ + αy + [u, α]⋆ − α ′ ) = 0. (4.13) − 3uy Hence we get α = −3∂ −1 x uy := −3 ∫ x uy(x ′ )dx ′ , and the NC KP equation =-=[6, 17]-=-: ( u ′′′ − 3 (u ′ ⋆ u + u ⋆ u ′ ) − 3∂ −1 x uyy − 3[u, ∂ −1 ) x uy]⋆ . (4.14) ˙u = 1 4 If we neglect y-dependence, the present discussion gives rise to another reduction to NC KdV equation from ASDYM... |

27 |
Noncommutative generalized NS and super matrix KdV systems from a noncommutative version of (anti-) selfdual Yang-Mills equations, Preprint hep-th/0012077
- Legaré
- 2000
(Show Context)
Citation Context ...ation under the reduction conditions: Q = i ( ) ( 1 0 0 ψ , Aw = 2 0 −1 ε ¯ ) ( ¯ψ ′ ⋆ ψ ψ , Az = i ψ 0 −ε ¯ ψ ′ −ψ ⋆ ¯ ) , (3.15) ψ where ε = ±1. The case for ε = −1 coincides with results by Legaré =-=[15]-=-. We note that the gauge group must be U(2) or U(1, 1) not SU(2) or SU(1, 1) on NC spaces because the matrix Az is not traceless. We prove that the choice by Legaré [15] is unique for the reduction an... |

25 |
Topological charge of U(1) instantons on noncommutative R**4,” Prog. Theor. Phys. Suppl
- Furuuchi
(Show Context)
Citation Context ...ished features of NC theories is resolution of singularities. This gives rise to various new physical objects such as U(1) instantons and makes it possible to analyze singular configurations as usual =-=[3]-=-. NC extension of integrable equations is also one of the hot topics and has been studied from various viewpoints by many authors [5]-[47]. These equations imply no gauge field and NC extension of the... |

18 |
A noncommutative version of the nonlinear Schroedinger equation,” hep-th/0007015
- Dimakis, Müller-Hoissen
(Show Context)
Citation Context ...˜ ψ. (3.12) By taking κ = i 2 , ˜ ψ = ¯ ψ, we get the NC repulsive NLS equation with G = U(1, 1): i ˙ ψ = ψ ′′ − 2ψ ⋆ ¯ ψ ⋆ ψ, (3.13) 5by taking κ = i 2 , ˜ ψ = − ¯ ψ, the NC attractive NLS equation =-=[8]-=- with G = U(2): i ˙ ψ = ψ ′′ + 2ψ ⋆ ¯ ψ ⋆ ψ. (3.14) In summary, only when a = b = 1, we can obtain the NC NLS equation by reduction of NC ASDYM equation under the reduction conditions: Q = i ( ) ( 1 0... |

10 |
Tachyon dynamics in open string theory,” hep-th/0410103
- Sen
(Show Context)
Citation Context ... succeeded in revealing various aspects of them [1]. NC solitons especially play important roles in the study of D-brane dynamics, such as the confirmation of Sen’s conjecture on tachyon condensation =-=[2]-=-. One of the distinguished features of NC theories is resolution of singularities. This gives rise to various new physical objects such as U(1) instantons and makes it possible to analyze singular con... |

9 | Extensions of soliton equations to non-commutative (2 + 1) dimensions - Toda - 2002 |

8 |
JHEP 0206
- Wolf
- 2002
(Show Context)
Citation Context ...nature. NC Yang-Mills theories with the split signature can be embedded [50] in N = 2 string theories [59]. Simple reductions of them and relation to the string theories have been studied intensively =-=[18, 22, 23, 29, 47]-=-. This guarantees that NC integrable equations would have physical meanings and might lead to various successful applications to the corresponding D-brane dynamics and so on. One of the next step is t... |

6 | Topics in nonlinear sigma models - Furuta, Inami, et al. |

5 | Burgers’ equation in non-commutative space-time,” hep-th/0302055 - Martina, Pashaev |

4 |
Noncommutative solitons and integrable systems,” hep-th/0504001
- Hamanaka
(Show Context)
Citation Context ...ew physical objects such as U(1) instantons and makes it possible to analyze singular configurations as usual [3]. NC extension of integrable equations is also one of the hot topics (For reviews, see =-=[4]-=-.) and has been studied from various viewpoints by many authors [5]-[47]. These equations imply no gauge field and NC extension of them perhaps might have no physical picture or no good property on in... |

4 | Matrix membranes and integrability - Zachos, Fairlie, et al. |

4 | A 37 (2004) 4069 [hep-th/0401142 - Dimakis, Müller-Hoissen, et al. |

4 |
Lechtenfeld O., Time-space noncommutative Abelian solitons, Phys
- Chu
(Show Context)
Citation Context ... makes it possible to analyze singular configurations as usual [3]. NC extension of integrable equations is also one of the hot topics and has been studied from various viewpoints by many authors [5]-=-=[47]-=-. These equations imply no gauge field and NC extension of them perhaps might have no physical picture or no good property on integrabilities. To make matters worse, NC extension of (1+1)-dimensional ... |

3 |
A 316 (2003) 77 [hep-th/0211148
- Lett
(Show Context)
Citation Context ...ities and the linearizability and so on. Furthermore, a few of them can be derived from NC (anti-)self-dual Yang-Mills (ASDYM) equations by suitable reductions, which is just an example of NC version =-=[27]-=- of Ward’s conjecture [48], that is, almost all NC integrable equations are reductions of NC ASDYM equations. (For commutative discussions, see e.g. [49, 50, 51, 52].) This makes it possible to give p... |

2 | 54 (2000) 123 [hep-th/0007160 - Phys |

1 | A 38 (2005) 5453 [nlin.si/0501003]; “Algebraic identities associated with KP and AKNS hierarchies,” math-ph/0507024 - Dimakis, Müller-Hoissen, et al. |