A self-dual Chern-Simons system and its Lax pair are derived from the tangent space representation of a two-dimensional nonlinear σ-model, endowed with a gauge field. The related “matter” field density obeys the Liouville equation, whose N-soliton solutions correspond to the magnetic vortices in the static self-dual planar Heisenberg model. It is shown that the topological charge and the total vorticity correspond to the electric charge and the magnetic flux for the Chern-Simons system, respectively. General holomorphic solutions of the system studied generate a large class of static solutions to the Davey-Stewartson and Ishimori equations.
Self-Dual Chern-Simons Solitons in Nonlinear σ-model
MARTINA, Luigi;SOLIANI, Giulio
1993-01-01
Abstract
A self-dual Chern-Simons system and its Lax pair are derived from the tangent space representation of a two-dimensional nonlinear σ-model, endowed with a gauge field. The related “matter” field density obeys the Liouville equation, whose N-soliton solutions correspond to the magnetic vortices in the static self-dual planar Heisenberg model. It is shown that the topological charge and the total vorticity correspond to the electric charge and the magnetic flux for the Chern-Simons system, respectively. General holomorphic solutions of the system studied generate a large class of static solutions to the Davey-Stewartson and Ishimori equations.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
