Rogue Waves generation by Using higher order rational solutions of Discrete Nonlinear Schrödinger Equation

Abstract

The higher-order discrete nonlinear Schrödinger equation has been demonstrated to be related to cubic-quintic nonlinearity. This executes the specified number of periodic solutions. The localized solution of the homogeneous cubic-quintic discrete nonlinear Schrödinger equation has been researched. By employing scaling transformations, it was possible to convert cubic-quintic discrete nonlinear Schrödinger equations to constant-coefficient higher-order rational solutions with discrete nonlinear Schrödinger equations (DNLSE). We investigated our solution in the periodic form of the gain/loss term and discovered some intriguing results. Even the solution is interconnected, and its features are extensively exploited in a variety of physical phenomena, including optical waveguides, B-E condensates in optical media, non-linearity in photonic crystals, Kerr-type nonlinearity and photo refracting medium.