2001/06/30 by Olaf Lechtenfeld, Alexander D. Popov · 1 citation
Mathematics · Physics and Astronomy · #Abelian group #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Factorization #Field (mathematics) #Integrable system #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Nonlinear system #Physics #Pure mathematics #Quantum mechanics #Sigma #Sigma model #Soliton #hep-th
paper · pdf · doi:10.1088/1126-6708/2001/11/040
published as JHEP 0111:040,2001 · 1+24 pages, no figures; v2: minor corrections, two references added; v3: typos corrected
openalex publication_date 2001/11/18 · arxiv created 2003/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The study of noncommutative solitons is greatly facilitated if the field equations are integrable, i.e. result from a linear system. For the example of a modified but integrable U(n) sigma model in 2+1 dimensions we employ the dressing method to construct explicit multi-soliton configurations on noncommutative R2,1. These solutions, abelian and nonabelian, feature exact time-dependence for any value of the noncommutativity parameter theta and describe various lumps of finite energy in relative motion. We discuss their scattering properties and prove asymptotic factorization for large times.