General rogue wave solutions to the discrete nonlinear Schr\"odinger equation
Yasuhiro Ohta, Bao-Feng Feng
TL;DR
This paper develops a method to construct general rogue wave solutions for the fully discrete nonlinear Schrödinger equation using KP-Toda reduction, starting from breather solutions and taking appropriate limits.
Contribution
It introduces a novel approach to derive rogue wave solutions for the discrete NLS equation via bilinear equations and reduction methods.
Findings
Derived general breather solutions for the fd-NLS equation.
Obtained rogue wave solutions through limiting procedures.
Provides a systematic framework for discrete rogue wave analysis.
Abstract
In the present paper, we attempt to construct both the general rogue wave solutions to the fully discrete nonlinear Schr\"odinger (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.
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