Multi-Soliton scattering of the Anti-Self-Dual Yang-Mills Equations in 4-dimensional split signature

TL;DR

This paper constructs multi-soliton solutions for the Anti-Self-Dual Yang-Mills equations in 4D split signature, revealing gauge group structures and interpreting solutions as soliton walls.

Contribution

It introduces explicit multi-soliton solutions for ASDYM equations in split signature and analyzes their gauge group properties and geometric interpretation.

Findings

Constructed ASDYM 1-solitons and multi-solitons in split signature

Identified gauge group as SU(2) for entire walls and SU(3) asymptotically

Interpreted solutions as soliton walls in 4D split signature

Abstract

We construct the ASDYM 1-solitons and multi-solitons for split signature and interpret them as soliton walls. We show that the gauge group is $\mathrm{G=SU(2)}$ for the entire intersecting soliton walls, and $\mathrm{SU(3)}$ for each soliton walls in the asymptotic region. This is joint research partially with Masashi Hamanaka, Claire R. Gilson, and Jonathan Nimmo.