2006/02/27 by Bo Dai, Chuu-Lian Terng, Dai, Bo +3 · 1 citation
Mathematics · Physics and Astronomy · #37K15 #37K25 #37K35 #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #math-ph #math.DG #math.MP #msc:37K15 #msc:37K25 #msc:37K35
paper · pdf · doi:10.48550/arxiv.math/0602607
31 pages
arxiv created 2006/02/27 · openalex publication_date 2006/02/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The space-time monopole equation is obtained from a dimension reduction of the anti-self dual Yang-Mills equation on \R2,2. A family of Ward equations is obtained by gauge fixing from the monopole equation. In this paper, we give an introduction and a survey of the space-time monopole equation. Included are alternative explanations of results of Ward, Fokas-Ioannidou, Villarroel and Zakhorov-Mikhailov. The equations are formulated in terms of a number of equivalent Lax pairs; we make use of the natural Lorentz action on the Lax pairs and frames. A new Hamiltonian formulation for the Ward equations is introduced. We outline both scattering and inverse scattering theory and use Bäcklund transformations to construct a large class of monopoles which are global in time and have both continuous and discrete scattering data.