Scattering of the vector soliton in coupled nonlinear schrodinger equation with gaussian potential
Nonlinear Schrodinger equation (NLSE) is the fundamental equation which describes the wave field envelope dynamics in a nonlinear and dispersive medium. However, if the fields have many components, one should consider the Coupled Nonlinear Schrodinger equation (CNLSE). We considered the interacti...
| Main Authors: | , , , , |
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| Format: | Proceeding Paper |
| Language: | English |
| Published: |
Malaysian Journal of Fundamental and Applied Sciences
2019
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/77000/ http://irep.iium.edu.my/77000/1/77000_Scattering%20of%20The%20Vector%20Soliton%20in%20Coupled_complete.pdf |
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| author | Mat Din, Mohd Azid Umarov, Bakhram A. Mohd Busul Aklan, Nor Amirah Busul Abdul Hadi, Muhammad Salihi Ismail, Nazmi Hakim |
| author_facet | Mat Din, Mohd Azid Umarov, Bakhram A. Mohd Busul Aklan, Nor Amirah Busul Abdul Hadi, Muhammad Salihi Ismail, Nazmi Hakim |
| author_sort | Mat Din, Mohd Azid |
| building | IIUM Repository |
| collection | Online Access |
| description | Nonlinear Schrodinger equation (NLSE) is the fundamental equation which describes the wave field
envelope dynamics in a nonlinear and dispersive medium. However, if the fields have many
components, one should consider the Coupled Nonlinear Schrodinger equation (CNLSE). We
considered the interactions of orthogonally polarized and equal-amplitude vector solitons with two
polarization directions. In this paper, we have been focussed on the effect of Gaussian potential on
the scattering of the vector soliton in CNLSE. The scattering process was investigated by the
variational approximation method and direct numerical solution of CNLSE. Analytically, we analysed
the dynamics of the width and center of mass position of a soliton by the variational approximation
method. Soliton may be reflected from each other or transmitted through or trapped. Initially,
uncoupled solitons may form the coupled state if the kinetic energy of solitons less than the potential
of attractive interaction between solitons but when its’ velocity (kinetic energy) above the critical
velocity, the soliton will pass through each other easily. Meanwhile, a direct numerical simulation of
CNLSE had been run to check the accuracy of the approximation. The result of the variational model
will give a slightly similar pattern with direct numerical simulation of CNLSE by fixing the parameters
for both solutions with the same value. The interaction of the vector soliton with Gaussian potential
depends on the initial velocity and amplitude of the soliton and the strength of the external potential. |
| first_indexed | 2025-11-14T17:39:46Z |
| format | Proceeding Paper |
| id | iium-77000 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T17:39:46Z |
| publishDate | 2019 |
| publisher | Malaysian Journal of Fundamental and Applied Sciences |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-770002020-01-10T09:13:38Z http://irep.iium.edu.my/77000/ Scattering of the vector soliton in coupled nonlinear schrodinger equation with gaussian potential Mat Din, Mohd Azid Umarov, Bakhram A. Mohd Busul Aklan, Nor Amirah Busul Abdul Hadi, Muhammad Salihi Ismail, Nazmi Hakim QA Mathematics QC Physics Nonlinear Schrodinger equation (NLSE) is the fundamental equation which describes the wave field envelope dynamics in a nonlinear and dispersive medium. However, if the fields have many components, one should consider the Coupled Nonlinear Schrodinger equation (CNLSE). We considered the interactions of orthogonally polarized and equal-amplitude vector solitons with two polarization directions. In this paper, we have been focussed on the effect of Gaussian potential on the scattering of the vector soliton in CNLSE. The scattering process was investigated by the variational approximation method and direct numerical solution of CNLSE. Analytically, we analysed the dynamics of the width and center of mass position of a soliton by the variational approximation method. Soliton may be reflected from each other or transmitted through or trapped. Initially, uncoupled solitons may form the coupled state if the kinetic energy of solitons less than the potential of attractive interaction between solitons but when its’ velocity (kinetic energy) above the critical velocity, the soliton will pass through each other easily. Meanwhile, a direct numerical simulation of CNLSE had been run to check the accuracy of the approximation. The result of the variational model will give a slightly similar pattern with direct numerical simulation of CNLSE by fixing the parameters for both solutions with the same value. The interaction of the vector soliton with Gaussian potential depends on the initial velocity and amplitude of the soliton and the strength of the external potential. Malaysian Journal of Fundamental and Applied Sciences 2019-08 Proceeding Paper PeerReviewed application/pdf en http://irep.iium.edu.my/77000/1/77000_Scattering%20of%20The%20Vector%20Soliton%20in%20Coupled_complete.pdf Mat Din, Mohd Azid and Umarov, Bakhram A. and Mohd Busul Aklan, Nor Amirah Busul and Abdul Hadi, Muhammad Salihi and Ismail, Nazmi Hakim (2019) Scattering of the vector soliton in coupled nonlinear schrodinger equation with gaussian potential. In: Workshop on Dynamical Systems and Their Applications in Mathematical Physics, Engineering, and Economics 2019 (WDS 2019), 26th-28th August 2019, Kuantan, Pahang. (Unpublished) |
| spellingShingle | QA Mathematics QC Physics Mat Din, Mohd Azid Umarov, Bakhram A. Mohd Busul Aklan, Nor Amirah Busul Abdul Hadi, Muhammad Salihi Ismail, Nazmi Hakim Scattering of the vector soliton in coupled nonlinear schrodinger equation with gaussian potential |
| title | Scattering of the vector soliton in coupled nonlinear schrodinger equation with gaussian potential |
| title_full | Scattering of the vector soliton in coupled nonlinear schrodinger equation with gaussian potential |
| title_fullStr | Scattering of the vector soliton in coupled nonlinear schrodinger equation with gaussian potential |
| title_full_unstemmed | Scattering of the vector soliton in coupled nonlinear schrodinger equation with gaussian potential |
| title_short | Scattering of the vector soliton in coupled nonlinear schrodinger equation with gaussian potential |
| title_sort | scattering of the vector soliton in coupled nonlinear schrodinger equation with gaussian potential |
| topic | QA Mathematics QC Physics |
| url | http://irep.iium.edu.my/77000/ http://irep.iium.edu.my/77000/1/77000_Scattering%20of%20The%20Vector%20Soliton%20in%20Coupled_complete.pdf |