Soliton Solutions and Nontrivial Scattering in an Integrable Chiral Model in (2+1) Dimensions

Abstract

The behaviour of solitons in integrable theories is strongly constrained by the integrability of the theory; i.e. by the existence of an infinite number of conserved quantities which these theories are known to possess. One usually expects the scattering of solitons in such theories to be rather simple, i.e. trivial. By contrast, in this paper we generate new soliton solutions for the planar integrable chiral model whose scattering properties are highly nontrivial; more precisely, in head-on collisions of $N$ indistinguishable solitons the scattering angle (of the emerging structures relative to the incoming ones) is $\pi /N$. We also generate soliton-antisoliton solutions with elastic scattering; in particular, a head-on collision of a soliton and an antisoliton resulting in $90^0$ scattering.

21 pages + 9 figures, LaTex (fingures are not included), to appear in Journal of Mathematical Physics

References in corpus (1)

• Nontrivial scattering of localized solitons in a (2+1)-dimensional integrable system

Cited by in corpus (26)

• Scattering of Noncommutative Solitons in 2+1 Dimensions
• Integrable Noncommutative Sine-Gordon Model
• Soliton-Antisoliton Scattering Configurations in a Noncommutative Sigma Model in 2+1 Dimensions
• Reduced dynamics of Ward solitons
• The Energy of Scattering Solitons in the Ward Model
• Topology and Energy of Time Dependent Unitons
• Solutions of the Modified Chiral Model in (2+1) Dimensions
• Ward's solitions
• Asymptotic dynamics of higher-order lumps in the Davey-Stewartson II equation
• Noncommutative Supersymmetric/Integrable Models and String Theory
• Moduli-Space Dynamics of Noncommutative Abelian Sigma-Model Solitons
• Exact time dependent Hopf solitons in 3+1 dimensions
• On the space-time Monopole equation
• Lagrangian Formulation of the General Modified Chiral Model
• A Note on Ward's Chiral Model
• Dispersionless limit of the noncommutative potential KP hierarchy and solutions of the pseudodual chiral model in 2+1 dimensions
• Integrable Yang-Mills-Higgs Equations in 3-Dimensional De Sitter Space-Time
• Compactified Twistor Fibration and Topology of Ward Unitons
• Bogomolny Yang-Mills-Higgs Solutions in (2+1) anti-de Sitter Space
• Scattering of Noncommutative Waves and Solitons in a Supersymmetric Chiral Model in 2+1 Dimensions
• Non-anticommutative solitons
• The Cauchy problem of the Ward equation with mixed scattering data
• The Cauchy Problem of the Ward equation
• Non-trivial Soliton Scattering in Planar Integrable Systems
• Applications of Loop Group Factorization to Geometric Soliton Equations
• Backlund transformations, Ward solitons, and unitons