Article ID Journal Published Year Pages File Type
1843420 Nuclear Physics B 2006 22 Pages PDF
Abstract
Non-commutative Ward's conjecture is a non-commutative version of the original Ward's conjecture which says that almost all integrable equations can be obtained from anti-self-dual Yang-Mills equations by reduction. In this paper, we prove that wide class of non-commutative integrable equations in both (2+1)- and (1+1)-dimensions are actually reductions of non-commutative anti-self-dual Yang-Mills equations with finite gauge groups, which include non-commutative versions of Calogero-Bogoyavlenskii-Schiff equation, Zakharov system, Ward's chiral and topological chiral models, (modified) Korteweg-de Vries, non-linear Schrödinger, Boussinesq, N-wave, (affine) Toda, sine-Gordon, Liouville, Tzitzéica, (Ward's) harmonic map equations, and so on. This would guarantee existence of twistor description of them and the corresponding physical situations in N=2 string theory, and lead to fruitful applications to non-commutative integrable systems and string theories. Some integrable aspects of them are also discussed.
Related Topics
Physical Sciences and Engineering Mathematics Mathematical Physics
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