Investigating wave solutions in coupled nonlinear Schrödinger equation: insights into bifurcation, chaos, and sensitivity
Abstract In this research, a systematic approach is employed to derive novel wave solutions for the coupled nonlinear Schrödinger equation. The transformation of the coupled partial differential equation into ordinary differential equation is achieved by utilizing a complex wave variable. Exponentia...
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| Format: | Article |
| Language: | English |
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Springer
2025-01-01
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| Series: | Discover Applied Sciences |
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| Online Access: | https://doi.org/10.1007/s42452-024-06359-2 |
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| author | Adil Jhangeer Abdallah M. Talafha Ariana Abdul Rahimzai Lubomír Říha |
| author_facet | Adil Jhangeer Abdallah M. Talafha Ariana Abdul Rahimzai Lubomír Říha |
| author_sort | Adil Jhangeer |
| collection | DOAJ |
| description | Abstract In this research, a systematic approach is employed to derive novel wave solutions for the coupled nonlinear Schrödinger equation. The transformation of the coupled partial differential equation into ordinary differential equation is achieved by utilizing a complex wave variable. Exponential function combinations are applied to construct the wave solutions. The accuracy of the derived solitons is validated through symbolic computations performed in Wolfram Mathematica, accompanied by graphical visualizations of the proposed solutions. The model is converted into a dynamical system, enabling qualitative and sensitivity analysis. Additionally, introducing perturbed terms is examined, revealing chaotic patterns in the system. The impact of variations in amplitude and frequency parameters on the system’s dynamical behaviour is thoroughly investigated. The findings underscore the efficiency and reliability of the applied techniques, demonstrating their applicability to a wide range of complex nonlinear systems. |
| format | Article |
| id | doaj-art-200633c5962a4590adf963da4bec4d60 |
| institution | Kabale University |
| issn | 3004-9261 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Springer |
| record_format | Article |
| series | Discover Applied Sciences |
| spelling | doaj-art-200633c5962a4590adf963da4bec4d602025-01-19T12:34:50ZengSpringerDiscover Applied Sciences3004-92612025-01-017111510.1007/s42452-024-06359-2Investigating wave solutions in coupled nonlinear Schrödinger equation: insights into bifurcation, chaos, and sensitivityAdil Jhangeer0Abdallah M. Talafha1Ariana Abdul Rahimzai2Lubomír Říha3IT4Innovations, VSB-Technical University of OstravaDepartment of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd UniversityDepartment of Mathematics Education Faculty, Laghman UniversityIT4Innovations, VSB-Technical University of OstravaAbstract In this research, a systematic approach is employed to derive novel wave solutions for the coupled nonlinear Schrödinger equation. The transformation of the coupled partial differential equation into ordinary differential equation is achieved by utilizing a complex wave variable. Exponential function combinations are applied to construct the wave solutions. The accuracy of the derived solitons is validated through symbolic computations performed in Wolfram Mathematica, accompanied by graphical visualizations of the proposed solutions. The model is converted into a dynamical system, enabling qualitative and sensitivity analysis. Additionally, introducing perturbed terms is examined, revealing chaotic patterns in the system. The impact of variations in amplitude and frequency parameters on the system’s dynamical behaviour is thoroughly investigated. The findings underscore the efficiency and reliability of the applied techniques, demonstrating their applicability to a wide range of complex nonlinear systems.https://doi.org/10.1007/s42452-024-06359-2Non-linear modelSensitivity evaluationChaotic dynamicsmGERFM |
| spellingShingle | Adil Jhangeer Abdallah M. Talafha Ariana Abdul Rahimzai Lubomír Říha Investigating wave solutions in coupled nonlinear Schrödinger equation: insights into bifurcation, chaos, and sensitivity Discover Applied Sciences Non-linear model Sensitivity evaluation Chaotic dynamics mGERFM |
| title | Investigating wave solutions in coupled nonlinear Schrödinger equation: insights into bifurcation, chaos, and sensitivity |
| title_full | Investigating wave solutions in coupled nonlinear Schrödinger equation: insights into bifurcation, chaos, and sensitivity |
| title_fullStr | Investigating wave solutions in coupled nonlinear Schrödinger equation: insights into bifurcation, chaos, and sensitivity |
| title_full_unstemmed | Investigating wave solutions in coupled nonlinear Schrödinger equation: insights into bifurcation, chaos, and sensitivity |
| title_short | Investigating wave solutions in coupled nonlinear Schrödinger equation: insights into bifurcation, chaos, and sensitivity |
| title_sort | investigating wave solutions in coupled nonlinear schrodinger equation insights into bifurcation chaos and sensitivity |
| topic | Non-linear model Sensitivity evaluation Chaotic dynamics mGERFM |
| url | https://doi.org/10.1007/s42452-024-06359-2 |
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