Solutions of the modified chiral model in (2+1) dimensions

Abstract

Abstract. This paper deals with classical solutions of the modified chiral model on R 2+1 . Such solutions are shown to correspond to products of various factor which we call time-dependent unitons. Then the problem of solving the system of second-order partial differential equations for the chiral field is reduced to solving a sequence of systems of first-order partial differential equations for the unitons.

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

“…While P ⋆ is given by T ⋆ , we can calculate the projectorP ⋆ using (3.33), therefore the field Φ ⋆ = (1 − 2P ⋆ ) ⋆ (1 − 2P ⋆ ) and hence, the energy density E ⋆ . Obviously, the solution (3.33) coincides in the limit θ → 0 with the one given by Ioannidou and Zakrzewski in [34]. Choosing m = n = 1, h 2 (z) = z 2 , h 3 (z) = 3 and therefore f = −2i(t + z 2 ) and g = −2i(t + 3), the solution (3.33) represents a three soliton configuration, which for large negative and positive times has a ring-like structure.…”

Energy of scattering solitons in the Ward model

“…This was actually noted earlier by Ioannidou & Zakrzewski (1998) in a few examples, but no proof was given. It is physically quite a surprising result, because the solutions represent solitons in motion and part of the energy is kinetic.…”

Sigma-Model Solitons in the Noncommutative Plane: Construction and Stability Analysis

“…These solutions have been discussed as static solutions of a 2+1 dimensional noncommutative sigma model [5,12,13,14] which results from Moyal deforming the WZWmodified integrable sigma model [15,16,17]. Here we review the results pertaining to the static situation.…”