Soliton equations in N-dimensions as exact reductions of Self-Dual Yang-Mills equation IV. The mM-LXII and Bogomolny equations

TL;DR

This paper explores the connection between multidimensional soliton equations and the Self-Dual Yang-Mills and Bogomolny equations, providing insights into their geometric and analytical structures.

Contribution

It establishes exact reductions of multidimensional soliton equations to well-known gauge theory equations, advancing understanding of their geometric origins.

Findings

Identifies specific reductions linking soliton equations to gauge theories

Clarifies the geometric interpretation of multidimensional soliton solutions

Provides a framework for analyzing soliton equations via gauge theory methods

Abstract

Some aspects of the multidimensional soliton geometry are considered. The relation between soliton equations in 2+1 dimensions and the Self-Dual Yang-Mills and Bogomolny equations are discussed.