Topology and Energy of Time Dependent Unitons

Abstract

We consider a class of time dependent finite energy multi-soliton solutions of the U(N) integrable chiral model in $(2+1)$ dimensions. The corresponding extended solutions of the associated linear problem have a pole with arbitrary multiplicity in the complex plane of the spectral parameter. Restrictions of these extended solutions to any spacelike plane in ${\mathbb{R}}^{2,1}$ have trivial monodromy and give rise to maps from a three sphere to U(N). We demonstrate that the total energy of each multi-soliton is quantised at the classical level and given by the third homotopy class of the extended solution. This is the first example of a topological mechanism explaining classical energy quantisation of moving solitons.

arXiv comment20 pages, one figure. References added and boundary conditions clarified. Final version, to appear in the Proceedings of the Royal Society A

References in corpus (8)

• Noncommutative Multi-Solitons in 2+1 Dimensions
• Scattering of Noncommutative Solitons in 2+1 Dimensions
• Nontrivial scattering of localized solitons in a (2+1)-dimensional integrable system
• Soliton Solutions and Nontrivial Scattering in an Integrable Chiral Model in (2+1) Dimensions
• Reduced dynamics of Ward solitons
• The Energy of Scattering Solitons in the Ward Model
• Solutions of the Modified Chiral Model in (2+1) Dimensions
• Ward's solitions

Cited by in corpus (4)

• Moduli spaces with external fields
• Dispersionless limit of the noncommutative potential KP hierarchy and solutions of the pseudodual chiral model in 2+1 dimensions
• Compactified Twistor Fibration and Topology of Ward Unitons
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