Effect of Cubic And Quintic Nonlinearities on Spatially Generated Rogue Waves In CQDNLSE

Abstract

The presence of soliton and multisoliton solutions have been postulated using various functional forms of Discrete nonlinear Schrödinger equation (DNLSE). These functional forms come from the inspiration that various terms represent different kind of nonlinearities in the system, and direct the behavior, characteristics, and propagation of rogue waves. Here cubic-quintic DNLSE (CQDNLSE) has been considered, and rogue waves are produced using various parameter combinations of the coefficients. The simulations consist of spatially discretizing the CQDNLS, put together with periodic boundary conditions, and Akhmediev -type initial conditions for rogue waves. Time propagation is obtained using RK4 method. The results show that the cubic and quintic terms enable the propagation of the rogue waves unidirectionally, but the presence of former leads to higher dissipation of energy along the waveguide. It is observed that rogue waves keep reappearing where the frequency of reappearance is significantly large when quintic terms dominate. Influence of sign dependence has been also observed and is reflected through the structure of the rogue wave, in the sense that the negative sign of the nonlinearities can help produce systems that are able to better control these waves, and as an example, find applications in waveguide design such as optical fibers.