We present exact soliton solutions of anti-self-dual Yang–Mills equations for G = GL ( N ) on noncommutative Euclidean spaces in four-dimension by using the Darboux transformations. Generated solutions are represented by quasideterminants of Wronski matrices in compact forms. We give special one-soliton solutions for G = GL (2) whose energy density can be real-valued. We find that the soliton solutions are the same as the commutative ones and can be interpreted as one-domain walls in four-dimension. Scattering processes of the multi-soliton solutions are also discussed.

中文翻译：

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非可交换反自对偶Yang-Mills方程的孤子解

我们通过使用Darboux变换，给出了四维非交换欧式空间上G = GL（N）的反自对偶Yang-Mills方程的精确孤子解。生成的解以紧凑形式的Wronski矩阵的四行列式表示。对于G = GL（2），我们给出了特殊的单孤子解，其能量密度可以是实值。我们发现孤子解与可交换解相同，并且可以解释为四维的一畴壁。还讨论了多孤子解的散射过程。