Two Analytical Schemes for the Optical Soliton Solution of the (2 + 1) Hirota–Maccari System Observed in Single-Mode Fibers
In this scientific research article, the new Kudryashov method and the tanh-coth method, which have not been applied before, are employed to construct analytical and soliton solutions of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-11-01
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| Series: | Universe |
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| Online Access: | https://www.mdpi.com/2218-1997/8/11/584 |
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| author | Neslihan Ozdemir Aydin Secer Muslum Ozisik Mustafa Bayram |
| author_facet | Neslihan Ozdemir Aydin Secer Muslum Ozisik Mustafa Bayram |
| author_sort | Neslihan Ozdemir |
| collection | DOAJ |
| description | In this scientific research article, the new Kudryashov method and the tanh-coth method, which have not been applied before, are employed to construct analytical and soliton solutions of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>-dimensional Hirota–Maccari system. The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>-dimensional Hirota–Maccari system is a special kind of nonlinear Schrödinger equation (NLSEs) that models the motion of isolated waves localized in a small part of space, and is used in such various fields as fiber optics telecommunication systems, nonlinear optics, plasma physics, and hydrodynamics. In addition, the Hirota–Maccari system defines the dynamical characters of femtosecond soliton pulse propagation in single-mode fibers. Analytical solutions of the model are successfully acquired with the assistance of symbolic computation utilizing these methods. Finally, 3D, 2D, and contour graphs of solutions are depicted at specific values of parameters. It is shown that the new Kudryashov method and the tanh-coth method are uncomplicated, very effective, easily applicable, reliable, and indeed vital mathematical tools in solving nonlinear models. |
| first_indexed | 2024-03-09T18:34:57Z |
| format | Article |
| id | doaj.art-1e7dede110ad4106b51a1b0f0aaeaf96 |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-09T18:34:57Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-1e7dede110ad4106b51a1b0f0aaeaf962023-11-24T07:12:21ZengMDPI AGUniverse2218-19972022-11-0181158410.3390/universe8110584Two Analytical Schemes for the Optical Soliton Solution of the (2 + 1) Hirota–Maccari System Observed in Single-Mode FibersNeslihan Ozdemir0Aydin Secer1Muslum Ozisik2Mustafa Bayram3Faculty of Engineering and Architecture, Istanbul Gelisim University, Istanbul 34310, TurkeyDepartment of Mathematics, Faculty of Science, Biruni University, Istanbul 34010, TurkeyDepartment of Mathematics Engineering, Faculty of Chemical and Metallurgical Engineering, Yildiz Technical University, Istanbul 34349, TurkeyDepartment of Computer Engineering, Biruni University, Istanbul 34010, TurkeyIn this scientific research article, the new Kudryashov method and the tanh-coth method, which have not been applied before, are employed to construct analytical and soliton solutions of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>-dimensional Hirota–Maccari system. The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>-dimensional Hirota–Maccari system is a special kind of nonlinear Schrödinger equation (NLSEs) that models the motion of isolated waves localized in a small part of space, and is used in such various fields as fiber optics telecommunication systems, nonlinear optics, plasma physics, and hydrodynamics. In addition, the Hirota–Maccari system defines the dynamical characters of femtosecond soliton pulse propagation in single-mode fibers. Analytical solutions of the model are successfully acquired with the assistance of symbolic computation utilizing these methods. Finally, 3D, 2D, and contour graphs of solutions are depicted at specific values of parameters. It is shown that the new Kudryashov method and the tanh-coth method are uncomplicated, very effective, easily applicable, reliable, and indeed vital mathematical tools in solving nonlinear models.https://www.mdpi.com/2218-1997/8/11/584new Kudryashov methodtanh-coth methodisolated wavessingle-mode fiberoptic soliton |
| spellingShingle | Neslihan Ozdemir Aydin Secer Muslum Ozisik Mustafa Bayram Two Analytical Schemes for the Optical Soliton Solution of the (2 + 1) Hirota–Maccari System Observed in Single-Mode Fibers Universe new Kudryashov method tanh-coth method isolated waves single-mode fiber optic soliton |
| title | Two Analytical Schemes for the Optical Soliton Solution of the (2 + 1) Hirota–Maccari System Observed in Single-Mode Fibers |
| title_full | Two Analytical Schemes for the Optical Soliton Solution of the (2 + 1) Hirota–Maccari System Observed in Single-Mode Fibers |
| title_fullStr | Two Analytical Schemes for the Optical Soliton Solution of the (2 + 1) Hirota–Maccari System Observed in Single-Mode Fibers |
| title_full_unstemmed | Two Analytical Schemes for the Optical Soliton Solution of the (2 + 1) Hirota–Maccari System Observed in Single-Mode Fibers |
| title_short | Two Analytical Schemes for the Optical Soliton Solution of the (2 + 1) Hirota–Maccari System Observed in Single-Mode Fibers |
| title_sort | two analytical schemes for the optical soliton solution of the 2 1 hirota maccari system observed in single mode fibers |
| topic | new Kudryashov method tanh-coth method isolated waves single-mode fiber optic soliton |
| url | https://www.mdpi.com/2218-1997/8/11/584 |
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