Bifurcation, chaos, modulation instability, and soliton analysis of the schrödinger equation with cubic nonlinearity
Abstract Bifurcation, chaos, modulation instability, and solitons are important phenomena in nonlinear dynamical structures that help us understand complex physical processes. This work employs the Schrödinger equation with cubic nonlinearity (SECN), rising in superconductivity, quantum mechanics, o...
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Nature Portfolio
2025-04-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-025-96327-6 |
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| author | Md. Shahidur Rahaman Mohammad Nazrul Islam Mohammad Safi Ullah |
| author_facet | Md. Shahidur Rahaman Mohammad Nazrul Islam Mohammad Safi Ullah |
| author_sort | Md. Shahidur Rahaman |
| collection | DOAJ |
| description | Abstract Bifurcation, chaos, modulation instability, and solitons are important phenomena in nonlinear dynamical structures that help us understand complex physical processes. This work employs the Schrödinger equation with cubic nonlinearity (SECN), rising in superconductivity, quantum mechanics, optics, and plasma physics. We developed an ordinary differential arrangement using a traveling wave alteration and found the soliton outcome to the mentioned problem utilizing the unified solver technique. Then we obtain different categories of wave designs, including bright and dark solitons, with periodic, quasiperiodic, and chaotic behaviors. We examined the system’s planar dynamics to observe sensitivity, chaos, and bifurcation. The chaotic state involves various procedures such as multistability, recurrence diagrams, bifurcation shapes, fractal dimensions, return maps, Poincaré graphics, Lyapunov exponents, phase portraits, and strange attractors. These properties help us understand complicated behaviors like how waves become chaotic patterns. Our outcomes demonstrate a clear understanding of wave propagation and how energy is absorbed. These findings develop our knowledge of nonlinear problems and guide us in wave circulation in real-life situations. Therefore, our procedures are useful and operative offering a simple technique for studying nonlinear problems, which progresses our understanding of these equations’ sensitivity, waveform pattern, and propagation strategy. |
| format | Article |
| id | doaj-art-e05c0afbdb6f415c94c8c80b076b5a1c |
| institution | DOAJ |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-e05c0afbdb6f415c94c8c80b076b5a1c2025-08-20T03:07:41ZengNature PortfolioScientific Reports2045-23222025-04-0115111310.1038/s41598-025-96327-6Bifurcation, chaos, modulation instability, and soliton analysis of the schrödinger equation with cubic nonlinearityMd. Shahidur Rahaman0Mohammad Nazrul Islam1Mohammad Safi Ullah2Department of Mathematics, Jahangirnagar UniversityDepartment of Mathematics, Jahangirnagar UniversityDepartment of Mathematics, Comilla UniversityAbstract Bifurcation, chaos, modulation instability, and solitons are important phenomena in nonlinear dynamical structures that help us understand complex physical processes. This work employs the Schrödinger equation with cubic nonlinearity (SECN), rising in superconductivity, quantum mechanics, optics, and plasma physics. We developed an ordinary differential arrangement using a traveling wave alteration and found the soliton outcome to the mentioned problem utilizing the unified solver technique. Then we obtain different categories of wave designs, including bright and dark solitons, with periodic, quasiperiodic, and chaotic behaviors. We examined the system’s planar dynamics to observe sensitivity, chaos, and bifurcation. The chaotic state involves various procedures such as multistability, recurrence diagrams, bifurcation shapes, fractal dimensions, return maps, Poincaré graphics, Lyapunov exponents, phase portraits, and strange attractors. These properties help us understand complicated behaviors like how waves become chaotic patterns. Our outcomes demonstrate a clear understanding of wave propagation and how energy is absorbed. These findings develop our knowledge of nonlinear problems and guide us in wave circulation in real-life situations. Therefore, our procedures are useful and operative offering a simple technique for studying nonlinear problems, which progresses our understanding of these equations’ sensitivity, waveform pattern, and propagation strategy.https://doi.org/10.1038/s41598-025-96327-6Unified solver procedureSensitivity assessmentLyapunov exponentStranger attractorBasins of attractionDynamical system |
| spellingShingle | Md. Shahidur Rahaman Mohammad Nazrul Islam Mohammad Safi Ullah Bifurcation, chaos, modulation instability, and soliton analysis of the schrödinger equation with cubic nonlinearity Scientific Reports Unified solver procedure Sensitivity assessment Lyapunov exponent Stranger attractor Basins of attraction Dynamical system |
| title | Bifurcation, chaos, modulation instability, and soliton analysis of the schrödinger equation with cubic nonlinearity |
| title_full | Bifurcation, chaos, modulation instability, and soliton analysis of the schrödinger equation with cubic nonlinearity |
| title_fullStr | Bifurcation, chaos, modulation instability, and soliton analysis of the schrödinger equation with cubic nonlinearity |
| title_full_unstemmed | Bifurcation, chaos, modulation instability, and soliton analysis of the schrödinger equation with cubic nonlinearity |
| title_short | Bifurcation, chaos, modulation instability, and soliton analysis of the schrödinger equation with cubic nonlinearity |
| title_sort | bifurcation chaos modulation instability and soliton analysis of the schrodinger equation with cubic nonlinearity |
| topic | Unified solver procedure Sensitivity assessment Lyapunov exponent Stranger attractor Basins of attraction Dynamical system |
| url | https://doi.org/10.1038/s41598-025-96327-6 |
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