Solitons in a one-dimensional discrete system with external potential

Researchers are currently investigating the impact of collisions between solitons and external potentials, particularly the Nonlinear Schrödinger Equation (NLSE), which governs the soliton interaction with the potential in the presence of nonlinearity. In the case of discrete systems of one-dimensio...

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Main Authors: Samiun, Anis Sulaikha, Mohd Busul Aklan, Nor Amirah, Umarov, Bakhram A.
Format: Proceeding Paper
Language:English
Published: AIP Publishing 2024
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Online Access:http://irep.iium.edu.my/113278/2/113278_Solitons%20in%20a%20one-dimensional%20discrete%20system%20with%20external%20potential.pdf
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Institution: Universiti Islam Antarabangsa Malaysia
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spelling my.iium.irep.1132782024-07-24T07:17:06Z http://irep.iium.edu.my/113278/ Solitons in a one-dimensional discrete system with external potential Samiun, Anis Sulaikha Mohd Busul Aklan, Nor Amirah Umarov, Bakhram A. QA Mathematics QA297 Numerical Analysis QC Physics Researchers are currently investigating the impact of collisions between solitons and external potentials, particularly the Nonlinear Schrödinger Equation (NLSE), which governs the soliton interaction with the potential in the presence of nonlinearity. In the case of discrete systems of one-dimensional NLSE, the behaviour and propagation of discrete solitons through a series of discrete sites or points are described. In this paper, we investigated the interaction of a discrete soliton with a localized impurity, namely the Gaussian external potential, using two methods: the variational approximation (VA) method and the direct numerical method. Discrete Cubic-Quintic NLSE is the main equation used to describe the phenomenon. This equation is non-integrable and does not have analytical solutions, but it can be reduced to ordinary differential equations using the variational approach. The VA method is applied by taking into account the Gaussian profile as the ansatz, which then produces evolution equations for soliton solutions of width, linear and quadratic phase-front correction and center-of-mass position. These equations play typical roles in describing the scattering process of the discrete soliton with the localized impurity. The direct numerical method of discrete NLSE is then performed to compare and validate the accuracy of the approximation results from the VA method. Considering different values of potential strengths and a fixed soliton initial velocity, it is found that the soliton can be transmitted, trapped or reflected after the interaction with external Gaussian potential. The findings imply that the VA method is a successful and practical way for examining the scattering of soliton in discrete NLSE on external potential. AIP Publishing 2024-07-12 Proceeding Paper PeerReviewed application/pdf en http://irep.iium.edu.my/113278/2/113278_Solitons%20in%20a%20one-dimensional%20discrete%20system%20with%20external%20potential.pdf Samiun, Anis Sulaikha and Mohd Busul Aklan, Nor Amirah and Umarov, Bakhram A. (2024) Solitons in a one-dimensional discrete system with external potential. In: The 4th International Conference on Applied & Industrial Mathematics and Statistics 2023 (ICoAIMS 2023), 22 - 24 August 2023, Hotel Grand DArul Makmur, Kuantan. https://pubs.aip.org/aip/acp/article-abstract/3128/1/020001/3303297/Solitons-in-a-one-dimensional-discrete-system-with?redirectedFrom=PDF
institution Universiti Islam Antarabangsa Malaysia
building IIUM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider International Islamic University Malaysia
content_source IIUM Repository (IREP)
url_provider http://irep.iium.edu.my/
language English
topic QA Mathematics
QA297 Numerical Analysis
QC Physics
spellingShingle QA Mathematics
QA297 Numerical Analysis
QC Physics
Samiun, Anis Sulaikha
Mohd Busul Aklan, Nor Amirah
Umarov, Bakhram A.
Solitons in a one-dimensional discrete system with external potential
description Researchers are currently investigating the impact of collisions between solitons and external potentials, particularly the Nonlinear Schrödinger Equation (NLSE), which governs the soliton interaction with the potential in the presence of nonlinearity. In the case of discrete systems of one-dimensional NLSE, the behaviour and propagation of discrete solitons through a series of discrete sites or points are described. In this paper, we investigated the interaction of a discrete soliton with a localized impurity, namely the Gaussian external potential, using two methods: the variational approximation (VA) method and the direct numerical method. Discrete Cubic-Quintic NLSE is the main equation used to describe the phenomenon. This equation is non-integrable and does not have analytical solutions, but it can be reduced to ordinary differential equations using the variational approach. The VA method is applied by taking into account the Gaussian profile as the ansatz, which then produces evolution equations for soliton solutions of width, linear and quadratic phase-front correction and center-of-mass position. These equations play typical roles in describing the scattering process of the discrete soliton with the localized impurity. The direct numerical method of discrete NLSE is then performed to compare and validate the accuracy of the approximation results from the VA method. Considering different values of potential strengths and a fixed soliton initial velocity, it is found that the soliton can be transmitted, trapped or reflected after the interaction with external Gaussian potential. The findings imply that the VA method is a successful and practical way for examining the scattering of soliton in discrete NLSE on external potential.
format Proceeding Paper
author Samiun, Anis Sulaikha
Mohd Busul Aklan, Nor Amirah
Umarov, Bakhram A.
author_facet Samiun, Anis Sulaikha
Mohd Busul Aklan, Nor Amirah
Umarov, Bakhram A.
author_sort Samiun, Anis Sulaikha
title Solitons in a one-dimensional discrete system with external potential
title_short Solitons in a one-dimensional discrete system with external potential
title_full Solitons in a one-dimensional discrete system with external potential
title_fullStr Solitons in a one-dimensional discrete system with external potential
title_full_unstemmed Solitons in a one-dimensional discrete system with external potential
title_sort solitons in a one-dimensional discrete system with external potential
publisher AIP Publishing
publishDate 2024
url http://irep.iium.edu.my/113278/2/113278_Solitons%20in%20a%20one-dimensional%20discrete%20system%20with%20external%20potential.pdf
http://irep.iium.edu.my/113278/
https://pubs.aip.org/aip/acp/article-abstract/3128/1/020001/3303297/Solitons-in-a-one-dimensional-discrete-system-with?redirectedFrom=PDF
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