Using the ∂̄-dressing method, we study the general reverse-space nonlocal nonlinear Schrödinger (nNLS) equation. Beginning with a 3 × 3 matrix ∂̄-problem, the associated spatial and time spectral problems are obtained through two linear constraint equations. Furthermore, the gauge equivalence between the Heisenberg chain equation and the general reverse-space nNLS equation is established. By employing a recursive operator, a hierarchy for the general reverse-space nNLS equation is proposed. Moreover, by selecting a suitable spectral transformation matrix, the N-soliton solutions of the general reverse-space nNLS equation are calculated, yielding the explicit one-soliton and two-soliton solutions.

中文翻译：

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一般逆空间非局部非线性薛定谔方程的 [公式省略] -修整方法和 [公式省略] -孤子解


使用 ∂̄ 敷料方法，我们研究了一般的逆空间非局部非线性薛定谔 （nNLS） 方程。从 3 × 3 矩阵 ∂̄ 问题开始，通过两个线性约束方程获得相关的空间和时间谱问题。此外，建立了 Heisenberg 链方程和一般逆空间 nNLS 方程之间的规范等效性。通过使用递归运算符，提出了一般反空间 nNLS 方程的层次结构。此外，通过选择合适的光谱变换矩阵，计算出一般反空间 nNLS 方程的 N 孤子解，得到明确的单孤子和双孤子解。