Higher-Dimensional Integrable Scattering

Abstract

This paper describes classical soliton scattering in the 2+1d integrable chiral model, related to the Bogomolny monopole equation and self-dual Yang-Mills, as a case study for higher-dimensional integrable scattering. Extended line solitons exhibit nontrivial scattering with lump solitons and with other line solitons, and $N\to N$ interactions can be factorised into a series of $2\to 2$ interactions. Scattering between parallel line solitons in 3d is related to lump soliton scattering in 2d, allowing for direct comparison with results in 1+1d integrable field theories.

34 pages, 9 figures