In the present paper, we attempt to construct both the general rogue wave solutions to the fully discrete nonlinear Schrödinger (fd-NLS) equation via the KP-Toda reduction method. First, we deduce the general breather solution of the fd-NLS equation starting from a pair of bilinear equations. We then derive the general rogue wave solution by taking a limit to the breather solution.
Ohta, Yasuhiro, and Bao-Feng Feng. "General rogue wave solutions to the discrete nonlinear Schrödinger equation." arXiv preprint arXiv:2201.02359 (2022).
Physica D: Nonlinear Phenomena