Dark soliton collisions and method of lines approach for modeling freak waves in a positron beam plasma having superthermal electrons
There are two main goals in this research, the first one is presenting an extended Poincaré–Lighthill–Kuo method (EPLKM) for studying the collisions between two dark envelope solitons in a non-Maxwellian plasma permeated by a positron beam, drawing inspiration from recent laboratory experiments on p...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2020-12-01
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| Series: | Results in Physics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379720319136 |
| _version_ | 1819074015632818176 |
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| author | S.A. El-Tantawy Mansoor H. Alshehri Faisal Z. Duraihem L.S. El-Sherif |
| author_facet | S.A. El-Tantawy Mansoor H. Alshehri Faisal Z. Duraihem L.S. El-Sherif |
| author_sort | S.A. El-Tantawy |
| collection | DOAJ |
| description | There are two main goals in this research, the first one is presenting an extended Poincaré–Lighthill–Kuo method (EPLKM) for studying the collisions between two dark envelope solitons in a non-Maxwellian plasma permeated by a positron beam, drawing inspiration from recent laboratory experiments on positron beams. The second goal in the present model explains the method of lines (MOLs) approach devoted for analyzing and modeling freak waves (FWs) . In order to achieve the goals of this study, a nonlinear Schrödinger equation (NLSE) has been derived using a reductive perturbation technique (RPT). The regions of (un)stable structures (dark and bright solitons and FWs) have been precisely defined based on the studying of modulational instability (MI) of the NLSE. In the stable regions, we focus our attention in examining and investigating dark soliton collisions. To do that a counterpart pair of two dark envelope solitons is assumed as initial condition, and EPLKM is employed to get expressions for the analytical phase shifts and determine the soliton trajectories after collisions. A parametric investigation is also presented by the effect of the superthermality (kappa) parameter and the positron beam characteristics (concentration, streaming velocity) on the colliding soliton properties. On the other side the MOLs approach is introduced for studying the rogue wave (RW) solution of the NLSE in the unstable regions. The numerical results of the comparison between the numerical and analytical solutions showed the accuracy of the MOLs. What prompted us to use this method is its high accuracy and ease of use rather than more complex numerical methods. These results will be helpful in understanding the dynamics of modulated structures (envelope dark soliton collisions and FWs) in purpose designed experiments. |
| first_indexed | 2024-12-21T18:02:48Z |
| format | Article |
| id | doaj.art-8254dece398f46b3a68a403c2104ba5e |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-12-21T18:02:48Z |
| publishDate | 2020-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-8254dece398f46b3a68a403c2104ba5e2022-12-21T18:55:01ZengElsevierResults in Physics2211-37972020-12-0119103452Dark soliton collisions and method of lines approach for modeling freak waves in a positron beam plasma having superthermal electronsS.A. El-Tantawy0Mansoor H. Alshehri1Faisal Z. Duraihem2L.S. El-Sherif3Department of Physics, Faculty of Science, Port Said University, Port Said 42521, Egypt; Research Center for Physics (RCP), Department of Physics, Faculty of Science and Arts, Al-Mikhwah, Al-Baha University, Saudi Arabia; Corresponding author at: Department of Physics, Faculty of Science, Port Said University, Port Said 42521, Egypt.Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Physics, College of Arts and Science, Prince Sattam bin Abdulaziz University, Wadi Al-Dawaser 11991, Saudi Arabia; Department of Physics, Faculty of Science, Ain Shams University, Cairo, EgyptThere are two main goals in this research, the first one is presenting an extended Poincaré–Lighthill–Kuo method (EPLKM) for studying the collisions between two dark envelope solitons in a non-Maxwellian plasma permeated by a positron beam, drawing inspiration from recent laboratory experiments on positron beams. The second goal in the present model explains the method of lines (MOLs) approach devoted for analyzing and modeling freak waves (FWs) . In order to achieve the goals of this study, a nonlinear Schrödinger equation (NLSE) has been derived using a reductive perturbation technique (RPT). The regions of (un)stable structures (dark and bright solitons and FWs) have been precisely defined based on the studying of modulational instability (MI) of the NLSE. In the stable regions, we focus our attention in examining and investigating dark soliton collisions. To do that a counterpart pair of two dark envelope solitons is assumed as initial condition, and EPLKM is employed to get expressions for the analytical phase shifts and determine the soliton trajectories after collisions. A parametric investigation is also presented by the effect of the superthermality (kappa) parameter and the positron beam characteristics (concentration, streaming velocity) on the colliding soliton properties. On the other side the MOLs approach is introduced for studying the rogue wave (RW) solution of the NLSE in the unstable regions. The numerical results of the comparison between the numerical and analytical solutions showed the accuracy of the MOLs. What prompted us to use this method is its high accuracy and ease of use rather than more complex numerical methods. These results will be helpful in understanding the dynamics of modulated structures (envelope dark soliton collisions and FWs) in purpose designed experiments.http://www.sciencedirect.com/science/article/pii/S2211379720319136Dark soliton collisionsPhase shiftsMethod of lines approachFreak wavesPositron beam plasmaSuperthermal electron |
| spellingShingle | S.A. El-Tantawy Mansoor H. Alshehri Faisal Z. Duraihem L.S. El-Sherif Dark soliton collisions and method of lines approach for modeling freak waves in a positron beam plasma having superthermal electrons Results in Physics Dark soliton collisions Phase shifts Method of lines approach Freak waves Positron beam plasma Superthermal electron |
| title | Dark soliton collisions and method of lines approach for modeling freak waves in a positron beam plasma having superthermal electrons |
| title_full | Dark soliton collisions and method of lines approach for modeling freak waves in a positron beam plasma having superthermal electrons |
| title_fullStr | Dark soliton collisions and method of lines approach for modeling freak waves in a positron beam plasma having superthermal electrons |
| title_full_unstemmed | Dark soliton collisions and method of lines approach for modeling freak waves in a positron beam plasma having superthermal electrons |
| title_short | Dark soliton collisions and method of lines approach for modeling freak waves in a positron beam plasma having superthermal electrons |
| title_sort | dark soliton collisions and method of lines approach for modeling freak waves in a positron beam plasma having superthermal electrons |
| topic | Dark soliton collisions Phase shifts Method of lines approach Freak waves Positron beam plasma Superthermal electron |
| url | http://www.sciencedirect.com/science/article/pii/S2211379720319136 |
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