A study on variational analysis: the discrete system in Cubic-Quintic non-linear Schrödinger equation - Mohd Yasin, Azyan Munirah; Mohd Busul Aklan, Nor Amirah (Department of Computational & Theoretical Sciences, International Islamic University Malaysia, 2024)
A system that experiences sudden state changes at specific times is said to be discrete. The majority of systems that are studied in operations research and management science, such as transportation or communication studies, are under the application of discrete systems. This study investigates the analytical study of the static soliton for Cubic-Quintic Discrete Nonlinear Schrödinger Equation (DNLSE) in discrete system. Subsequently, static soliton, that is often used to characterize specific self-action regime in a continuous one-dimensional problem, is defined as a self-reinforcing wave packet that keeps its form and velocity while it travels in a medium. Moreover, it is well-known that the NLSE is a known integrable equation of partial differential equation. Therefore, the variational approximation method is applied to convert partial differential equations into ordinary differential equations, thus, to derive the equations for soliton parameters evolution during the interaction process. The method is used for qualitative study of Discrete NLSE and classify selfaction modes. The diffraction of narrow (in grating scale) wave beams weakens in discrete media is demonstrated, leading to the “collapse” of the one-dimensional wave field with power exceeding the critical value. As a result, the central fiber gains the ability to self-channel radiation.