Breather and solitonic behavior of parametric Sine–Gordon equation with phase-shift and driven term
This study presents a comprehensive analytical and computational investigation of the nonlinear parametric sine-Gordon equation (sGE) with a driven term and phase shift. The sGE model captures the current and voltage dynamics across a weak connection between two superconductors, providing valuable i...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-03-01
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| Series: | Results in Physics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379725000324 |
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| author | Taj Munir Muhammad Zaman Can Kang Hussan Zeb Alrazi Abdeljabbar Mohammed Daher Albalwi |
| author_facet | Taj Munir Muhammad Zaman Can Kang Hussan Zeb Alrazi Abdeljabbar Mohammed Daher Albalwi |
| author_sort | Taj Munir |
| collection | DOAJ |
| description | This study presents a comprehensive analytical and computational investigation of the nonlinear parametric sine-Gordon equation (sGE) with a driven term and phase shift. The sGE model captures the current and voltage dynamics across a weak connection between two superconductors, providing valuable insights into the behavior of Josephson Junction systems. To validate the results, two primary methodologies are employed for approximating solutions to the sGE. Analytically, a perturbative expansion combined with multiple-scale analysis is developed to derive system dynamics up to the fifth-order expansion. Numerically, the explicit finite difference scheme and the fourth-order Runge–Kutta finite difference method are implemented. The model equation is formulated for a 0−π−0 junction with appropriate initial and boundary conditions. Furthermore, the stability of the numerical scheme is rigorously analyzed, accounting for constraints imposed by the nonlinear terms. The findings reveal that the breathing modes of oscillation decay towards a constant state, with strong agreement observed between the analytical and numerical results. Additionally, one- and two-dimensional numerical computations are performed to enhance the clarity and depth of the analysis. This research significantly contributes to the fields of superconductivity and nonlinear dynamics, offering novel insights into the complex behavior of coupled systems and advancing the understanding of Josephson Junction dynamics. |
| format | Article |
| id | doaj-art-a3bc0dce53c84514ab25bf69870d1a2a |
| institution | Kabale University |
| issn | 2211-3797 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj-art-a3bc0dce53c84514ab25bf69870d1a2a2025-02-08T05:00:21ZengElsevierResults in Physics2211-37972025-03-0170108138Breather and solitonic behavior of parametric Sine–Gordon equation with phase-shift and driven termTaj Munir0Muhammad Zaman1Can Kang2Hussan Zeb3Alrazi Abdeljabbar4Mohammed Daher Albalwi5School of Energy and Power Engineering, Jiangsu University, Zhenjiang, 212013, PR ChinaDepartment of Higher Education, Khyber Pakhtunkhwa, PakistanSchool of Energy and Power Engineering, Jiangsu University, Zhenjiang, 212013, PR China; Corresponding authors.Department of Mathematics Hazara University, PakistanDepartment of Mathematics, Khalifa University of Science and Technology, Abu Dhabi 127788, United Arab Emirates; Corresponding authors.Yanbu Industrial College, The Royal Commission for Jubail and Yanbu, 30436, Saudi ArabiaThis study presents a comprehensive analytical and computational investigation of the nonlinear parametric sine-Gordon equation (sGE) with a driven term and phase shift. The sGE model captures the current and voltage dynamics across a weak connection between two superconductors, providing valuable insights into the behavior of Josephson Junction systems. To validate the results, two primary methodologies are employed for approximating solutions to the sGE. Analytically, a perturbative expansion combined with multiple-scale analysis is developed to derive system dynamics up to the fifth-order expansion. Numerically, the explicit finite difference scheme and the fourth-order Runge–Kutta finite difference method are implemented. The model equation is formulated for a 0−π−0 junction with appropriate initial and boundary conditions. Furthermore, the stability of the numerical scheme is rigorously analyzed, accounting for constraints imposed by the nonlinear terms. The findings reveal that the breathing modes of oscillation decay towards a constant state, with strong agreement observed between the analytical and numerical results. Additionally, one- and two-dimensional numerical computations are performed to enhance the clarity and depth of the analysis. This research significantly contributes to the fields of superconductivity and nonlinear dynamics, offering novel insights into the complex behavior of coupled systems and advancing the understanding of Josephson Junction dynamics.http://www.sciencedirect.com/science/article/pii/S2211379725000324Soliton and breather solutionPerturbation with multiple-scale expansionJosephson junctionExplicit finite difference and RK-4 scheme0-π-0 junction |
| spellingShingle | Taj Munir Muhammad Zaman Can Kang Hussan Zeb Alrazi Abdeljabbar Mohammed Daher Albalwi Breather and solitonic behavior of parametric Sine–Gordon equation with phase-shift and driven term Results in Physics Soliton and breather solution Perturbation with multiple-scale expansion Josephson junction Explicit finite difference and RK-4 scheme 0-π-0 junction |
| title | Breather and solitonic behavior of parametric Sine–Gordon equation with phase-shift and driven term |
| title_full | Breather and solitonic behavior of parametric Sine–Gordon equation with phase-shift and driven term |
| title_fullStr | Breather and solitonic behavior of parametric Sine–Gordon equation with phase-shift and driven term |
| title_full_unstemmed | Breather and solitonic behavior of parametric Sine–Gordon equation with phase-shift and driven term |
| title_short | Breather and solitonic behavior of parametric Sine–Gordon equation with phase-shift and driven term |
| title_sort | breather and solitonic behavior of parametric sine gordon equation with phase shift and driven term |
| topic | Soliton and breather solution Perturbation with multiple-scale expansion Josephson junction Explicit finite difference and RK-4 scheme 0-π-0 junction |
| url | http://www.sciencedirect.com/science/article/pii/S2211379725000324 |
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