Exploring conversation laws and nonlinear dynamics of the unstable nonlinear Schrödinger equation: Stability and applications
The nonlinear Schrödinger equation (NLSE) is a fundamental nonlinear model renowned for its accurate description of light pulse propagation in optical fibers. The unstable NLSE, a universal equation in nonlinear integrable systems, governs instabilities in modulated wave trains and characterizes the...
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| Language: | English |
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Elsevier
2025-01-01
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| Series: | Ain Shams Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2090447924005914 |
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| author | Muhammad Arshad Muhammad Attar Umer Changjin Xu Abdulrahman A. Almehizia Faisal Yasin |
| author_facet | Muhammad Arshad Muhammad Attar Umer Changjin Xu Abdulrahman A. Almehizia Faisal Yasin |
| author_sort | Muhammad Arshad |
| collection | DOAJ |
| description | The nonlinear Schrödinger equation (NLSE) is a fundamental nonlinear model renowned for its accurate description of light pulse propagation in optical fibers. The unstable NLSE, a universal equation in nonlinear integrable systems, governs instabilities in modulated wave trains and characterizes the temporal progression of disturbances in near-stable or unstable media. This article analytically explores the nonlinear dynamics of the uNLSE, employing three symbolic computation methods: the three-wave (TW) approach, the positive-quadratic function (PQF) approach, and the double exponential (DE) approach. Our analysis yields novel exact solutions and multi-wave solutions, including rational solitons, breathers, and various wave types associated with this model. These results are derived using the ansatz function method and symbolic computation, including transformations involving logarithmic and traveling waves. The wave solutions obtained significantly deepen our apprehension of the physical phenomena within this intricate model. Additionally, we computed conserved quantities such as momentum, power, and energy associated with the solitons. The modulational instability (MI) analysis is utilized to evaluate the stability of the uNLSE, which confirmed the exactness and stability of all soliton solutions. Through the selection of appropriate parameter values, we produced 3D and contour visualizations in forms such as lump waves, breather-sort waves, and multi-peak solitons. |
| format | Article |
| id | doaj-art-4bc2c83660b047a4a9a515d1de72278b |
| institution | Kabale University |
| issn | 2090-4479 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Ain Shams Engineering Journal |
| spelling | doaj-art-4bc2c83660b047a4a9a515d1de72278b2025-01-17T04:49:25ZengElsevierAin Shams Engineering Journal2090-44792025-01-01161103210Exploring conversation laws and nonlinear dynamics of the unstable nonlinear Schrödinger equation: Stability and applicationsMuhammad Arshad0Muhammad Attar Umer1Changjin Xu2Abdulrahman A. Almehizia3Faisal Yasin4Department of Mathematics and Statistics, University of Agriculture Faisalabad, Pakistan; Corresponding author.Department of Mathematics and Statistics, University of Agriculture Faisalabad, PakistanGuizhou key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang 550025, PR ChinaDepartment of Pharmaceutical Chemistry, College of Pharmacy, King Saud University, PO Box 2457, Riyadh 11451, Saudi ArabiaDepartment of Mathematics and Statistics, The University of Lahore, Lahore Campus, PakistanThe nonlinear Schrödinger equation (NLSE) is a fundamental nonlinear model renowned for its accurate description of light pulse propagation in optical fibers. The unstable NLSE, a universal equation in nonlinear integrable systems, governs instabilities in modulated wave trains and characterizes the temporal progression of disturbances in near-stable or unstable media. This article analytically explores the nonlinear dynamics of the uNLSE, employing three symbolic computation methods: the three-wave (TW) approach, the positive-quadratic function (PQF) approach, and the double exponential (DE) approach. Our analysis yields novel exact solutions and multi-wave solutions, including rational solitons, breathers, and various wave types associated with this model. These results are derived using the ansatz function method and symbolic computation, including transformations involving logarithmic and traveling waves. The wave solutions obtained significantly deepen our apprehension of the physical phenomena within this intricate model. Additionally, we computed conserved quantities such as momentum, power, and energy associated with the solitons. The modulational instability (MI) analysis is utilized to evaluate the stability of the uNLSE, which confirmed the exactness and stability of all soliton solutions. Through the selection of appropriate parameter values, we produced 3D and contour visualizations in forms such as lump waves, breather-sort waves, and multi-peak solitons.http://www.sciencedirect.com/science/article/pii/S2090447924005914Unstable nonlinear Schrödinger equationSymbolic computational methodsRational and multi soliton solutionsConversation lawsStability |
| spellingShingle | Muhammad Arshad Muhammad Attar Umer Changjin Xu Abdulrahman A. Almehizia Faisal Yasin Exploring conversation laws and nonlinear dynamics of the unstable nonlinear Schrödinger equation: Stability and applications Ain Shams Engineering Journal Unstable nonlinear Schrödinger equation Symbolic computational methods Rational and multi soliton solutions Conversation laws Stability |
| title | Exploring conversation laws and nonlinear dynamics of the unstable nonlinear Schrödinger equation: Stability and applications |
| title_full | Exploring conversation laws and nonlinear dynamics of the unstable nonlinear Schrödinger equation: Stability and applications |
| title_fullStr | Exploring conversation laws and nonlinear dynamics of the unstable nonlinear Schrödinger equation: Stability and applications |
| title_full_unstemmed | Exploring conversation laws and nonlinear dynamics of the unstable nonlinear Schrödinger equation: Stability and applications |
| title_short | Exploring conversation laws and nonlinear dynamics of the unstable nonlinear Schrödinger equation: Stability and applications |
| title_sort | exploring conversation laws and nonlinear dynamics of the unstable nonlinear schrodinger equation stability and applications |
| topic | Unstable nonlinear Schrödinger equation Symbolic computational methods Rational and multi soliton solutions Conversation laws Stability |
| url | http://www.sciencedirect.com/science/article/pii/S2090447924005914 |
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