In this paper we revisit the $(2+1)$-dimensional mixed AKNS hierarchy recently studied by Gürses and Pekcan (2019, 2021). We present a unified bilinear form for the whole hierarchy and solutions in double Wronskian form. Local and nonlocal reductions of the hierarchy are considered and explicit $N$-soliton solutions for the reduced equations are obtained by means of a reduction technique on double Wronskians.

中文翻译：

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在 (2+1) 维混合 AKNS 层次结构上

在本文中，我们重新审视 $(2+1)$Gürses 和 Pekcan (2019, 2021) 最近研究的维混合 AKNS 层次结构。我们以双 Wronskian 形式为整个层次结构和解决方案提供了一个统一的双线性形式。层次结构的局部和非局部减少被考虑和明确$N$简化方程的孤子解是通过对双 Wronskian 的简化技术获得的。