Study of nonlinear wave equation of optical field for solotonic type results
This paper uses the fractional perturbed Gerdjikov–Ivanov (PGI) model, a basic mathematical framework in mathematical physics and nonlinear dynamics, to examine complex wave structures using the M-fractional operator and modified Extended Direct Algebraic Method (mEDAM). We find a wide variety of ne...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-03-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818124004340 |
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| author | Ikram Ullah Muhammad Bilal Dawood Shah Hasib Khan Jehad Alzabut Hisham Mohammad Alkhawar |
| author_facet | Ikram Ullah Muhammad Bilal Dawood Shah Hasib Khan Jehad Alzabut Hisham Mohammad Alkhawar |
| author_sort | Ikram Ullah |
| collection | DOAJ |
| description | This paper uses the fractional perturbed Gerdjikov–Ivanov (PGI) model, a basic mathematical framework in mathematical physics and nonlinear dynamics, to examine complex wave structures using the M-fractional operator and modified Extended Direct Algebraic Method (mEDAM). We find a wide variety of new optical wave solutions, such as kink-type, dark, brilliant, periodic, combo, exponential, trigonometric, and hyperbolic solutions. our examine the dynamic behavior and free parameters of these soliton solutions using contour plots and three-dimensional charts. The uniqueness of the study is shown by the noteworthy consistency and divergence of our results from earlier answers. This work makes a substantial contribution to the PGI model’s ability to extract many solitary wave solutions. The proposed suggested method shows dependability while assessing analytical solutions for fractional differential equations. This research intends to extend mathematical approaches for solving fractional differential equations, which will enable answers to a wide range of practical scientific and engineering problems, including implications for ultrafast pulse transmission in optical fibers. |
| format | Article |
| id | doaj-art-282762b7cdbf489093104548371b8f5d |
| institution | Kabale University |
| issn | 2666-8181 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-282762b7cdbf489093104548371b8f5d2025-01-08T04:53:45ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812025-03-0113101048Study of nonlinear wave equation of optical field for solotonic type resultsIkram Ullah0Muhammad Bilal1Dawood Shah2Hasib Khan3Jehad Alzabut4Hisham Mohammad Alkhawar5School of Mathematics and Statistics, Central South University, Changsha 410083, Hunan, PR China; Corresponding author.Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Khyber Pukhton Khwkha, PakistanDepartment of Mathematics, University of Malakand, Dir Lower 18000, Khyber Pukhton Khwkha, PakistanDepartment of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, 11586 Riyadh, Saudi Arabia; Department of Mathematics, Shaheed Benazir Bhutto Uniersity, Sheringal, Dir Upper, 18000, Khyber Pakhtunkhwa, PakistanDepartment of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, 11586 Riyadh, Saudi Arabia; Department of Industrial Engineering, OSTIM Technical University, 06374 Ankara, Turkiye; Center for Research and Innovation, Asia International University, Yangiobod MFY, G’ijduvon street, House 74 Bukhara, UzbekistanPreparatory Year Program, Computer Department, Prince Sultan University, 11586 Riyadh, Saudi ArabiaThis paper uses the fractional perturbed Gerdjikov–Ivanov (PGI) model, a basic mathematical framework in mathematical physics and nonlinear dynamics, to examine complex wave structures using the M-fractional operator and modified Extended Direct Algebraic Method (mEDAM). We find a wide variety of new optical wave solutions, such as kink-type, dark, brilliant, periodic, combo, exponential, trigonometric, and hyperbolic solutions. our examine the dynamic behavior and free parameters of these soliton solutions using contour plots and three-dimensional charts. The uniqueness of the study is shown by the noteworthy consistency and divergence of our results from earlier answers. This work makes a substantial contribution to the PGI model’s ability to extract many solitary wave solutions. The proposed suggested method shows dependability while assessing analytical solutions for fractional differential equations. This research intends to extend mathematical approaches for solving fractional differential equations, which will enable answers to a wide range of practical scientific and engineering problems, including implications for ultrafast pulse transmission in optical fibers.http://www.sciencedirect.com/science/article/pii/S2666818124004340Fractional differential equationsModified Extended Direct Algebraic Method (mEDAM)Fractional perturbed Gerdjikov–Ivanov (PGI) modelNonlinear opticsSolitary wave solutionsAdvancements in mathematical modeling |
| spellingShingle | Ikram Ullah Muhammad Bilal Dawood Shah Hasib Khan Jehad Alzabut Hisham Mohammad Alkhawar Study of nonlinear wave equation of optical field for solotonic type results Partial Differential Equations in Applied Mathematics Fractional differential equations Modified Extended Direct Algebraic Method (mEDAM) Fractional perturbed Gerdjikov–Ivanov (PGI) model Nonlinear optics Solitary wave solutions Advancements in mathematical modeling |
| title | Study of nonlinear wave equation of optical field for solotonic type results |
| title_full | Study of nonlinear wave equation of optical field for solotonic type results |
| title_fullStr | Study of nonlinear wave equation of optical field for solotonic type results |
| title_full_unstemmed | Study of nonlinear wave equation of optical field for solotonic type results |
| title_short | Study of nonlinear wave equation of optical field for solotonic type results |
| title_sort | study of nonlinear wave equation of optical field for solotonic type results |
| topic | Fractional differential equations Modified Extended Direct Algebraic Method (mEDAM) Fractional perturbed Gerdjikov–Ivanov (PGI) model Nonlinear optics Solitary wave solutions Advancements in mathematical modeling |
| url | http://www.sciencedirect.com/science/article/pii/S2666818124004340 |
| work_keys_str_mv | AT ikramullah studyofnonlinearwaveequationofopticalfieldforsolotonictyperesults AT muhammadbilal studyofnonlinearwaveequationofopticalfieldforsolotonictyperesults AT dawoodshah studyofnonlinearwaveequationofopticalfieldforsolotonictyperesults AT hasibkhan studyofnonlinearwaveequationofopticalfieldforsolotonictyperesults AT jehadalzabut studyofnonlinearwaveequationofopticalfieldforsolotonictyperesults AT hishammohammadalkhawar studyofnonlinearwaveequationofopticalfieldforsolotonictyperesults |