Applications of two novel techniques in finding optical soliton solutions of modified nonlinear Schrödinger equations
Finding optical soliton solutions to nonlinear partial differential equations has become a popular topic in recent decades. The primary goal of this study is to identify a diverse collection of wave solutions to a generalized version of the nonlinear Schrödinger equation. We investigate two modifica...
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| Format: | Article |
| Language: | English |
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Elsevier
2023-01-01
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| Series: | Results in Physics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379722007926 |
| _version_ | 1797950749508894720 |
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| author | Behzad Ghanbari Dumitru Baleanu |
| author_facet | Behzad Ghanbari Dumitru Baleanu |
| author_sort | Behzad Ghanbari |
| collection | DOAJ |
| description | Finding optical soliton solutions to nonlinear partial differential equations has become a popular topic in recent decades. The primary goal of this study is to identify a diverse collection of wave solutions to a generalized version of the nonlinear Schrödinger equation. We investigate two modifications to the generalized exponential rational function method to derive the expected results for this model. The first method is primarily based on using elementary functions such as exponential, trigonometric, and hyperbolic forms, which are commonly used to calculate the results. As for the second method, it is based on applying Jacobi elliptic functions to formulate solutions, whereas the underlying idea is the same as with the first method. As a means of enhancing the reader’s understanding of the results, we plot the graphical properties of our solutions. Based on this article’s results, it can be concluded that both techniques are easy to follow, and yet very efficient. These integration methods can determine different categories of solutions all in a unified framework. Therefore, it can be concluded from the manuscript that the approaches adopted in the manuscript may be regarded as efficient tools for determining wave solutions of a variety of partial differential equations. Due to the high computational complexity, the main requirement for applying our proposed methods is to employ an efficient computing software. Here, symbolic packages in Wolfram Mathematica have been used to validate the entire results of the paper. |
| first_indexed | 2024-04-10T22:20:03Z |
| format | Article |
| id | doaj.art-ac10abf526cd4933bbb2d8e7fb407cbb |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-04-10T22:20:03Z |
| publishDate | 2023-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-ac10abf526cd4933bbb2d8e7fb407cbb2023-01-18T04:30:39ZengElsevierResults in Physics2211-37972023-01-0144106171Applications of two novel techniques in finding optical soliton solutions of modified nonlinear Schrödinger equationsBehzad Ghanbari0Dumitru Baleanu1Department of Basic Science, Kermanshah University of Technology, Kermanshah, Iran; Corresponding author.Department of Mathematics, Cankaya University, Balgat 06530, Ankara, Turkey; Institute of Space Sciences, R76900 Magurele-Bucharest, Romania; Department of Medical Research, China Medical University, Taichung 40402, TaiwanFinding optical soliton solutions to nonlinear partial differential equations has become a popular topic in recent decades. The primary goal of this study is to identify a diverse collection of wave solutions to a generalized version of the nonlinear Schrödinger equation. We investigate two modifications to the generalized exponential rational function method to derive the expected results for this model. The first method is primarily based on using elementary functions such as exponential, trigonometric, and hyperbolic forms, which are commonly used to calculate the results. As for the second method, it is based on applying Jacobi elliptic functions to formulate solutions, whereas the underlying idea is the same as with the first method. As a means of enhancing the reader’s understanding of the results, we plot the graphical properties of our solutions. Based on this article’s results, it can be concluded that both techniques are easy to follow, and yet very efficient. These integration methods can determine different categories of solutions all in a unified framework. Therefore, it can be concluded from the manuscript that the approaches adopted in the manuscript may be regarded as efficient tools for determining wave solutions of a variety of partial differential equations. Due to the high computational complexity, the main requirement for applying our proposed methods is to employ an efficient computing software. Here, symbolic packages in Wolfram Mathematica have been used to validate the entire results of the paper.http://www.sciencedirect.com/science/article/pii/S2211379722007926Wave solitonsNonlinear Schrödinger equationPlasma modelsNumerical structures |
| spellingShingle | Behzad Ghanbari Dumitru Baleanu Applications of two novel techniques in finding optical soliton solutions of modified nonlinear Schrödinger equations Results in Physics Wave solitons Nonlinear Schrödinger equation Plasma models Numerical structures |
| title | Applications of two novel techniques in finding optical soliton solutions of modified nonlinear Schrödinger equations |
| title_full | Applications of two novel techniques in finding optical soliton solutions of modified nonlinear Schrödinger equations |
| title_fullStr | Applications of two novel techniques in finding optical soliton solutions of modified nonlinear Schrödinger equations |
| title_full_unstemmed | Applications of two novel techniques in finding optical soliton solutions of modified nonlinear Schrödinger equations |
| title_short | Applications of two novel techniques in finding optical soliton solutions of modified nonlinear Schrödinger equations |
| title_sort | applications of two novel techniques in finding optical soliton solutions of modified nonlinear schrodinger equations |
| topic | Wave solitons Nonlinear Schrödinger equation Plasma models Numerical structures |
| url | http://www.sciencedirect.com/science/article/pii/S2211379722007926 |
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