From discrete nonlocal nonlinear Schrödinger equation to coupled discrete Heisenberg ferromagnet equation. (August 2022) - Ma, Li-Yuan; Shen, Shou-Feng; Zhu, Zuo-Nong
Abstract: The investigation of nonlocal reverse space, reverse time, and reverse space–time integrable equations becomes an interesting and hot topic. In the paper Ma and Zhu (2016), we have shown that the nonlocal focusing nonlinear Schrödinger (NLS) equation, the nonlocal defocusing NLS equation and their discrete versions are, respectively gauge equivalent to a Heisenberg ferromagnet (HF)-like equation, and a modified HF-like equation and their corresponding discrete cases. In this paper, we further show that the HF-like equation and the modified HF-like equation essentially are the coupled HF equation and the coupled HF-type equation in Minkowski space. We give a connection of the discrete coupled HF equation and the discrete coupled HF-type equation in Minkowski space and the corresponding coupled HF equation and coupled HF-type equation in Minkowski space. This means that the nonlocal focusing and defocusing NLS equations are gauge equivalent to the coupled HF and coupled HF-type equation in Minkowski space. The solution of the coupled HF-type equation in Minkowski space is constructed.