General rogue wave solution to the discrete nonlinear Schrödinger equation

In the present paper, we are concerned with the rogue wave solution to an integrable discrete nonlinear Schrödinger (NLS) equation. First, through the KP–Toda reduction method, the general breather solution of the discrete NLS equation is deduced from two bilinear equations in discrete two-dimensional Toda-lattice hierarchy. Then, by taking an ingenious and successive limit to the breather solution, we derive the higher order rogue wave solution to the discrete NLS equation.