A study on variational analysis: the discrete system in Cubic-Quintic non-linear Schrödinger equation

Mohd Yasin, Azyan Munirah and Mohd Busul Aklan, Nor Amirah (2024) A study on variational analysis: the discrete system in Cubic-Quintic non-linear Schrödinger equation. In: Final Year Project 2023/2024 Seminar, 17 January 2024, IIUM Kuantan.

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Abstract

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.

Item Type:	Proceeding Paper (Poster)
Uncontrolled Keywords:	Discrete stationary soliton, cubic-quintic nonlinear Schrödinger equation, variational approximation method, wave scattering process
Subjects:	Q Science > QA Mathematics Q Science > QA Mathematics > QA297 Numerical Analysis Q Science > QC Physics T Technology > T Technology (General)
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User:	Dr Nor Amirah Mohd Busul Aklan
Date Deposited:	29 Mar 2024 14:56
Last Modified:	29 Mar 2024 16:10
URI:	http://irep.iium.edu.my/id/eprint/111588

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