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dc.contributor.authorPashaev, Oktay
dc.contributor.authorGürkan, Zeynep Nilhan
dc.date.accessioned2016-08-12T10:47:38Z
dc.date.available2016-08-12T10:47:38Z
dc.date.issued2007-07
dc.identifier.citationPashaev, O., and Gürkan, Z. N. (2007). Abelian Chern-Simons vortices and holomorphic Burgers hierarchy. Theoretical and Mathematical Physics, 152(1), 1017-1029. doi:10.1007/s11232-007-0086-0en_US
dc.identifier.issn0040-5779
dc.identifier.urihttp://doi.org/10.1007/s11232-007-0086-0
dc.identifier.urihttp://hdl.handle.net/11147/2093
dc.description.abstractWe consider the Abelian Chern-Simons gauge field theory in 2+1 dimensions and its relation to the holomorphic Burgers hierarchy. We show that the relation between the complex potential and the complex gauge field as in incompressible and irrotational hydrodynamics has the meaning of the analytic Cole-Hopf transformation, linearizing the Burgers hierarchy and transforming it into the holomorphic Schrödinger hierarchy. The motion of planar vortices in Chern-Simons theory, which appear as pole singularities of the gauge field, then corresponds to the motion of zeros of the hierarchy. We use boost transformations of the complex Galilei group of the hierarchy to construct a rich set of exact solutions describing the integrable dynamics of planar vortices and vortex lattices in terms of generalized Kampe de Feriet and Hermite polynomials. We apply the results to the holomorphic reduction of the Ishimori model and the corresponding hierarchy, describing the dynamics of magnetic vortices and the corresponding lattices in terms of complexified Calogero-Moser models. We find corrections (in terms of Airy functions) to the two-vortex dynamics from the Moyal space-time noncommutativity.en_US
dc.language.isoengen_US
dc.publisherSpringeren_US
dc.relation.isversionof10.1007/s11232-007-0086-0en_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectBurgers hierarchyen_US
dc.subjectChern-Simons gauge theoryen_US
dc.subjectHolomorphic equationen_US
dc.subjectIshimori modelen_US
dc.subjectKampe de Feriet polynomialen_US
dc.subjectNoncommutative vortexen_US
dc.titleAbelian Chern-Simons vortices and holomorphic Burgers hierarchyen_US
dc.typeconferenceObjecten_US
dc.contributor.authorIDTR57865en_US
dc.contributor.authorIDTR14029en_US
dc.contributor.iztechauthorPashaev, Oktay
dc.contributor.iztechauthorGürkan, Zeynep Nilhan
dc.relation.journalTheoretical and Mathematical Physicsen_US
dc.contributor.departmentIzmir Institute of Technology. Mathematicsen_US
dc.identifier.volume152en_US
dc.identifier.issue1en_US
dc.identifier.startpage1017en_US
dc.identifier.endpage1029en_US
dc.identifier.wosWOS:000249207000014
dc.identifier.scopusSCOPUS:2-s2.0-34548397234
dc.relation.publicationcategoryKonferans Öğesi - Uluslararası - Kurum Öğretim Elemanıen_US


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