Optical soliton solutions, bifurcation analysis, chaotic behaviors of nonlinear Schrödinger equation and modulation instability in optical fiber
In this study, we use the powerful and strong method to obtain a solution of the Sasa–Satsuma equation as (ℋ+G′G2)\left({\mathcal{ {\mathcal H} }}+\frac{{{\mathcal{G}}}^{^{\prime} }}{{{\mathcal{G}}}^{2}})-expansion method. This method plays a considerable role in solving nonlinear partial differenti...
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| Format: | Article |
| Language: | English |
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De Gruyter
2025-06-01
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| Series: | Open Physics |
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| Online Access: | https://doi.org/10.1515/phys-2025-0164 |
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| author | Ali Khalid K. Adel Tasneem Abd El-Salam Mansour N. Mohamed Mohamed S. Shaalan Mohamed A. |
| author_facet | Ali Khalid K. Adel Tasneem Abd El-Salam Mansour N. Mohamed Mohamed S. Shaalan Mohamed A. |
| author_sort | Ali Khalid K. |
| collection | DOAJ |
| description | In this study, we use the powerful and strong method to obtain a solution of the Sasa–Satsuma equation as (ℋ+G′G2)\left({\mathcal{ {\mathcal H} }}+\frac{{{\mathcal{G}}}^{^{\prime} }}{{{\mathcal{G}}}^{2}})-expansion method. This method plays a considerable role in solving nonlinear partial differential equations (NPDEs). We investigate the modulation instability in higher-order NPDEs. Modulation instability is a phenomenon observed in certain types of nonlinear systems, such as optical fiber or plasma waves. Modulation instability is a key process in generating optical solitons, rogue waves, and interest in various fields such as nonlinear optics and plasma physics. Using a linearizing technique, we establish the modulation instability and show the influence of a higher nonlinear component in modulation instability. We examine the bifurcation analysis of the Sasa–Satsuma equation. The time histories and Poincare mapping are used to scrutinize the chaotic behaviors of the dynamical system of the Sasa–Satsuma equation excited by a parametric excitation force. To control the vibrating system, use proportional feedback control (P-Controller). Two-dimensional and three-dimensional figures are presented for singular, dark, and bright optical soliton solutions related to optical fiber. These graphs are very important and useful in describing the behavior of solutions. |
| format | Article |
| id | doaj-art-4b27e63b7d854decadeee8a1bd2f1019 |
| institution | OA Journals |
| issn | 2391-5471 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Physics |
| spelling | doaj-art-4b27e63b7d854decadeee8a1bd2f10192025-08-20T02:34:16ZengDe GruyterOpen Physics2391-54712025-06-012312172310.1515/phys-2025-0164Optical soliton solutions, bifurcation analysis, chaotic behaviors of nonlinear Schrödinger equation and modulation instability in optical fiberAli Khalid K.0Adel Tasneem1Abd El-Salam Mansour N.2Mohamed Mohamed S.3Shaalan Mohamed A.4Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, EgyptAl-Obour Higher Institute for Engineering and Technology, Al Obour City, EgyptHigher Technological Institute, Tenth of Ramadan City, EgyptDepartment of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif, 21944, Saudi ArabiaHigher Technological Institute, Tenth of Ramadan City, EgyptIn this study, we use the powerful and strong method to obtain a solution of the Sasa–Satsuma equation as (ℋ+G′G2)\left({\mathcal{ {\mathcal H} }}+\frac{{{\mathcal{G}}}^{^{\prime} }}{{{\mathcal{G}}}^{2}})-expansion method. This method plays a considerable role in solving nonlinear partial differential equations (NPDEs). We investigate the modulation instability in higher-order NPDEs. Modulation instability is a phenomenon observed in certain types of nonlinear systems, such as optical fiber or plasma waves. Modulation instability is a key process in generating optical solitons, rogue waves, and interest in various fields such as nonlinear optics and plasma physics. Using a linearizing technique, we establish the modulation instability and show the influence of a higher nonlinear component in modulation instability. We examine the bifurcation analysis of the Sasa–Satsuma equation. The time histories and Poincare mapping are used to scrutinize the chaotic behaviors of the dynamical system of the Sasa–Satsuma equation excited by a parametric excitation force. To control the vibrating system, use proportional feedback control (P-Controller). Two-dimensional and three-dimensional figures are presented for singular, dark, and bright optical soliton solutions related to optical fiber. These graphs are very important and useful in describing the behavior of solutions.https://doi.org/10.1515/phys-2025-0164sasa–satsuma equation(ℋ + g′/g2)-expansion methodnonlinear optical systemqualitative analysisdynamical systemp-controller |
| spellingShingle | Ali Khalid K. Adel Tasneem Abd El-Salam Mansour N. Mohamed Mohamed S. Shaalan Mohamed A. Optical soliton solutions, bifurcation analysis, chaotic behaviors of nonlinear Schrödinger equation and modulation instability in optical fiber Open Physics sasa–satsuma equation (ℋ + g′/g2)-expansion method nonlinear optical system qualitative analysis dynamical system p-controller |
| title | Optical soliton solutions, bifurcation analysis, chaotic behaviors of nonlinear Schrödinger equation and modulation instability in optical fiber |
| title_full | Optical soliton solutions, bifurcation analysis, chaotic behaviors of nonlinear Schrödinger equation and modulation instability in optical fiber |
| title_fullStr | Optical soliton solutions, bifurcation analysis, chaotic behaviors of nonlinear Schrödinger equation and modulation instability in optical fiber |
| title_full_unstemmed | Optical soliton solutions, bifurcation analysis, chaotic behaviors of nonlinear Schrödinger equation and modulation instability in optical fiber |
| title_short | Optical soliton solutions, bifurcation analysis, chaotic behaviors of nonlinear Schrödinger equation and modulation instability in optical fiber |
| title_sort | optical soliton solutions bifurcation analysis chaotic behaviors of nonlinear schrodinger equation and modulation instability in optical fiber |
| topic | sasa–satsuma equation (ℋ + g′/g2)-expansion method nonlinear optical system qualitative analysis dynamical system p-controller |
| url | https://doi.org/10.1515/phys-2025-0164 |
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