Exploring the chaotic, sensitivity and wave patterns to the dual-mode resonant Schrödinger equation: application in optical engineering
Abstract The comprehension of nonlinear problems is essential for the understanding of nonlinear wave propagation in applied sciences. This work investigates the dual-mode manifestation within the nonlinear Schrodinger equation, clarifying the amplification or absorption of coupled waves. This inves...
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Nature Portfolio
2025-08-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-025-99654-w |
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| author | Jan Muhammad Usman Younas Mohammad Yar |
| author_facet | Jan Muhammad Usman Younas Mohammad Yar |
| author_sort | Jan Muhammad |
| collection | DOAJ |
| description | Abstract The comprehension of nonlinear problems is essential for the understanding of nonlinear wave propagation in applied sciences. This work investigates the dual-mode manifestation within the nonlinear Schrodinger equation, clarifying the amplification or absorption of coupled waves. This investigation explores the dual-mode phenomenon’s simultaneous generation of two distinct waves, which are influenced by three critical parameters: phase velocity, nonlinearity, and dispersive factor. By utilizing the complex wave transformation, we derive the nonlinear ordinary differential equation of the governing model. Additionally, we employ recently developed analytical techniques, including the modified generalized exponential rational function method and the multivariate generalized exponential rational integral function method, to find a wide range of solutions such as bright-dark, bright, dark, and combined solitons for the proposed model. Moreover, the chaotic and sensitivity analysis are discussed. Different graphs are included to clarify the behavior of solutions for several parameter values. |
| format | Article |
| id | doaj-art-2cb8f4aa42b94453b5c0260af6cebf42 |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-2cb8f4aa42b94453b5c0260af6cebf422025-08-24T11:30:39ZengNature PortfolioScientific Reports2045-23222025-08-0115112310.1038/s41598-025-99654-wExploring the chaotic, sensitivity and wave patterns to the dual-mode resonant Schrödinger equation: application in optical engineeringJan Muhammad0Usman Younas1Mohammad Yar2Department of Mathematics, Shanghai UniversityDepartment of Mathematics, Shanghai UniversityDepartment of Mathematics, Kabul Polytechnic UniversityAbstract The comprehension of nonlinear problems is essential for the understanding of nonlinear wave propagation in applied sciences. This work investigates the dual-mode manifestation within the nonlinear Schrodinger equation, clarifying the amplification or absorption of coupled waves. This investigation explores the dual-mode phenomenon’s simultaneous generation of two distinct waves, which are influenced by three critical parameters: phase velocity, nonlinearity, and dispersive factor. By utilizing the complex wave transformation, we derive the nonlinear ordinary differential equation of the governing model. Additionally, we employ recently developed analytical techniques, including the modified generalized exponential rational function method and the multivariate generalized exponential rational integral function method, to find a wide range of solutions such as bright-dark, bright, dark, and combined solitons for the proposed model. Moreover, the chaotic and sensitivity analysis are discussed. Different graphs are included to clarify the behavior of solutions for several parameter values.https://doi.org/10.1038/s41598-025-99654-wModified generalized exponential rational function methodMultivariate generalized exponential rational integral function techniqueSolitonsDual-mode Schrödinger equationKerr lawSquare root Kerr law |
| spellingShingle | Jan Muhammad Usman Younas Mohammad Yar Exploring the chaotic, sensitivity and wave patterns to the dual-mode resonant Schrödinger equation: application in optical engineering Scientific Reports Modified generalized exponential rational function method Multivariate generalized exponential rational integral function technique Solitons Dual-mode Schrödinger equation Kerr law Square root Kerr law |
| title | Exploring the chaotic, sensitivity and wave patterns to the dual-mode resonant Schrödinger equation: application in optical engineering |
| title_full | Exploring the chaotic, sensitivity and wave patterns to the dual-mode resonant Schrödinger equation: application in optical engineering |
| title_fullStr | Exploring the chaotic, sensitivity and wave patterns to the dual-mode resonant Schrödinger equation: application in optical engineering |
| title_full_unstemmed | Exploring the chaotic, sensitivity and wave patterns to the dual-mode resonant Schrödinger equation: application in optical engineering |
| title_short | Exploring the chaotic, sensitivity and wave patterns to the dual-mode resonant Schrödinger equation: application in optical engineering |
| title_sort | exploring the chaotic sensitivity and wave patterns to the dual mode resonant schrodinger equation application in optical engineering |
| topic | Modified generalized exponential rational function method Multivariate generalized exponential rational integral function technique Solitons Dual-mode Schrödinger equation Kerr law Square root Kerr law |
| url | https://doi.org/10.1038/s41598-025-99654-w |
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