Abstract
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.
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