\(N\)-soliton-type solutions of the self-dual Yang-Mills equations in \(M^ 4\) (Q1918814)

The purpose of this paper is to study the \(N\)-soliton-type solutions of the self-dual Yang-Mills (sdYM) equations in \(M^4\), and the case \(N = 2\) by using computers. The authors discuss the sdYM equations in Minkowski spacetime \(M^4\), \[ F_{\mu \nu} = {1\over 2} i \varepsilon_{\mu v \alpha \beta} F^{\alpha \beta} \tag{1} \] where \[ F_{\mu \nu} = \partial_\mu A_\nu - \partial_\nu A_\mu + [A_\mu, A_\nu] \tag{2} \] and \(\varepsilon_{\mu \nu \alpha \beta}\) is the totally antisymmetric 4-tensor. They present two ways of obtaining exact \(N\)-soliton-type solutions of equations (1) and (2), construct a regular spherically symmetric one-soliton-type solution of (1), and give a corresponding \(N\)-soliton-type generalization.