Comparative Study of Rogue Wave Solutions for Autonomous and Non-autonomous Saturable Discrete Nonlinear Schrödinger Equation

The existence of rogue waves in the saturable discrete nonlinear Schrodinger equation (SDNLSE) has been established numerically. These extreme waves are created using the Runge–Kutta 4 algorithm. The implementation of this technique is extended further to generate rogue waves for non-autonomous SDNLSE. The time dependence of the nonlinearity coefficient has been observed to play a significant role in manipulating the behavior of rogue waves. Three specific time dependences have been investigated. The periodic variation causes the rogue waves to split among various lattice points, whereas this wave channels along one direction as a result of the kink-shaped variation, and the intensity of the wave also rises due to this change. In contrast to these two Lorentzian variations of the nonlinearity coefficient results in the spread of the rogue waves at the lattice point, lowering the peak strength.