Reduced dynamics of Ward solitons

Abstract

The moduli space of static finite energy solutions to Ward's integrable chiral model is the space $M_N$ of based rational maps from $\CP^1$ to itself with degree $N$. The Lagrangian of Ward's model gives rise to a Kähler metric and a magnetic vector potential on this space. However, the magnetic field strength vanishes, and the approximate non--relativistic solutions to Ward's model correspond to a geodesic motion on $M_N$. These solutions can be compared with exact solutions which describe non--scattering or scattering solitons.

arXiv commentFinal version, to appear in Nonlinearity

References in corpus (6)

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• The L^2 geometry of spaces of harmonic maps S^2 -> S^2 and RP^2 -> RP^2
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Cited by in corpus (10)

• Topology and Energy of Time Dependent Unitons
• Moduli spaces with external fields
• Moduli-Space Dynamics of Noncommutative Abelian Sigma-Model Solitons
• Dispersionless limit of the noncommutative potential KP hierarchy and solutions of the pseudodual chiral model in 2+1 dimensions
• $\ast$-SDYM fields and heavenly spaces: II. Reductions of the $\ast$-SDYM system
• Noncommutative Solitons
• Dynamics of two interacting kinks for the ${\varphi }^6$ model
• Scattering of Noncommutative Waves and Solitons in a Supersymmetric Chiral Model in 2+1 Dimensions
• On the late phase of relaxation of two-dimensional fluids: turbulence of unitons
• Noncommutative deformation of the Ward metric