Soliton-Antisoliton Scattering Configurations in a Noncommutative Sigma Model in 2+1 Dimensions

2002/04/30 by Martin Wolf · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Collision #Computer science #Extension (predicate logic) #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Nonlinear system #Physics #Quantum mechanics #Scattering #Sigma #Sigma model #Soliton #hep-th

paper · pdf · doi:10.1088/1126-6708/2002/06/055

published as JHEP 0206:055,2002 · v.2: two references added, minor corrections

openalex publication_date 2002/06/28 · arxiv created 2002/07/08 · arxiv updated 2014/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

In this paper we study the noncommutative extension of a modified U(n) sigma model in 2+1 dimensions. Using the method of dressing transformations, an iterative approach for the construction of solutions from a given seed solution, we demonstrate the construction of multi-soliton and soliton-antisoliton configurations for general n. As illustrative examples we discuss U(3) solitons and consider the head-on collision of a U(2) soliton and an antisoliton explicitly, which will result in a 90^o angle scattering. Further we discuss the head-on collision of one U(2) soliton with two antisolitons. This results in a 60^o angle scattering.

Citations

• Komaba Lectures on Noncommutative Solitons and D-Branes
• String theory and noncommutative geometry
• Flux tube solutions in noncommutative gauge theories
• Instantons on Noncommutative ℝ 4 , and (2,0) Superconformal Six Dimensional Theory
• Restrictions on gauge groups in noncommutative gauge theory
• Nontrivial scattering of localized solitons in a (2+1)-dimensional integrable system

Cited by

• Noncommutative Solitons
• Lax pair and Darboux transformation of a noncommutativeU(N) principal chiral model