On the space-time Monopole equation
| dc.creator | Dai, Bo | |
| dc.creator | Terng, Chuu-Lian | |
| dc.creator | Uhlenbeck, Karen | |
| dc.date | 2006-02-27 | |
| dc.date.accessioned | 2026-07-07T07:03:49Z | |
| dc.date.available | 2026-07-07T07:03:49Z | |
| dc.description | The space-time monopole equation is obtained from a dimension reduction of the anti-self dual Yang-Mills equation on $\R^{2,2}$. 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. | |
| dc.description | 31 pages | |
| dc.identifier | https://arxiv.org/abs/math/0602607 | |
| dc.identifier | http://arxiv.org/abs/math/0602607 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/109125 | |
| dc.subject | Differential Geometry | |
| dc.subject | Mathematical Physics | |
| dc.subject | 37K15, 37K25, 37K35 | |
| dc.title | On the space-time Monopole equation | |
| dc.type | text |