Time-Space Noncommutative Abelian Solitons

Abstract

We demonstrate the construction of solitons for a time-space Moyal-deformed integrable U(n) sigma model (the Ward model) in 2+1 dimensions. These solitons cannot travel parallel to the noncommutative spatial direction. For the U(1) case, the rank-one single-soliton configuration is constructed explicitly and is singular in the commutative limit. The projection to 1+1 dimensions reduces it to a noncommutative instanton-like configuration. The latter is governed by a new integrable equation, which describes a Moyal-deformed sigma model with a particular Euclidean metric and a magnetic field.

1+10 pages

References in corpus (3)

• Integrable Noncommutative Sine-Gordon Model
• Sigma-Model Solitons in the Noncommutative Plane: Construction and Stability Analysis
• Noncommutative Solitons and Integrable Systems

Cited by in corpus (12)

• Noncommutative Ward's Conjecture and Integrable Systems
• On Reductions of Noncommutative Anti-Self-Dual Yang-Mills Equations
• Quantum Aspects of the Noncommutative Sine-Gordon Model
• Dispersionless limit of the noncommutative potential KP hierarchy and solutions of the pseudodual chiral model in 2+1 dimensions
• Noncommutative Solitons in a Supersymmetric Chiral Model in 2+1 Dimensions
• Emergence of Time from Dimensional Reduction in Noncommutative Geometry
• Noncommutative Solitons
• The noncommutative sine-Gordon breather
• Non-anticommutative solitons
• Noncommutative Nonlinear Sigma Models and Integrability
• The Noncommutative Ward Metric
• Supersymmetric noncommutative solitons