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In this thesis, we construct a class of exact ASDYM 1-solitons andmulti-solitons on 4-dimensional real spaces with the Euclidean signature $(+,+, +, +)$, the Minkowski signature $(+, - , -, -)$, and the split signature($+$, $+$, $-$, $-$) (the Ultrahyperbolic space). They are new results andsuccessful applications of the Darboux transformation introduced by Nimmo,Gilson, Ohta. In particular, the principal peak of the Lagrangian densityTr$F_{\mu\nu}F^{\mu\nu}$ is localized on a 3-dimensional hyperplane in 4dimensional space. Therefore, we use the term "soliton walls" to distinguishthem from the domain walls. For the split signature, we show that the gaugegroup can be $G=\mathrm{SU}(2)$ and $G=\mathrm{SU}(3)$ and hence the solitonwalls could be candidates of physically interesting objects on theUltrahyperbolic space $\mathbb{U}$. On the other hand, we use the techniques ofthe quasideterminants to show that in the asymptotic region, the ASDYM$n$-soliton possesses $n$ isolated distributions of Lagrangian densities withphase shifts. Therefore, we can interpret it as $n$ intersecting soliton walls.

On Soliton Solutions of the Anti-Self-Dual Yang-Mills Equations from the Perspective of Integrable Systems