Modulation instability, and dynamical behavior of solitary wave solution of time M- fractional clannish random Walker's Parabolic equation via two analytic techniques
The theory of solitary waves or solitons is crucial in nonlinear models due to their ability to propagate without distortion, making them essential in fields like physics, biology, engineering, and mathematics. This study explores solitary waves in the time fractional Clannish Random Walker's P...
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Elsevier
2024-12-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818124003978 |
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| author | Mohammed Kbiri Alaoui Mahtab Uddin Md. Mamunur Roshid Harun Or Roshid M.S. Osman |
| author_facet | Mohammed Kbiri Alaoui Mahtab Uddin Md. Mamunur Roshid Harun Or Roshid M.S. Osman |
| author_sort | Mohammed Kbiri Alaoui |
| collection | DOAJ |
| description | The theory of solitary waves or solitons is crucial in nonlinear models due to their ability to propagate without distortion, making them essential in fields like physics, biology, engineering, and mathematics. This study explores solitary waves in the time fractional Clannish Random Walker's Parabolic equation using two effective approaches: polynomial expansion technique (PET) and unified technique (UT). This model is particularly significant in areas such as ecology, sociology, and urban planning, where understanding individual interactions within spatial contexts is vital. By solving this equation, we gain insights into group formation and navigation, enhancing our comprehension of emergent patterns and system design. The application of PET and UT allows us to derive various solutions, including exponential, hyperbolic, and trigonometric forms. Utilizing the Maple programming language, we visualize novel phenomena, such as kink waves, anti-kink waves, and periodic lump waves. This research demonstrates that the proposed methodologies can yield precise soliton solutions, contributing valuable insights to nonlinear science and engineering applications. |
| format | Article |
| id | doaj-art-de1330eef1aa4c0a86bdfca3a424d228 |
| institution | OA Journals |
| issn | 2666-8181 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-de1330eef1aa4c0a86bdfca3a424d2282025-08-20T02:38:10ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812024-12-011210101110.1016/j.padiff.2024.101011Modulation instability, and dynamical behavior of solitary wave solution of time M- fractional clannish random Walker's Parabolic equation via two analytic techniquesMohammed Kbiri Alaoui0Mahtab Uddin1Md. Mamunur Roshid2Harun Or Roshid3M.S. Osman4Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi ArabiaInstitute of Natural Sciences, United International University, Dhaka, BangladeshDepartment of Mathematics, Hamdard University Bangladesh, Munshiganj, Bangladesh; Corresponding author.Department of Mathematics, Sunamgonj Science and Technology University, Shantiganj, Sunamganj 300, BangladeshDepartment of Mathematics, Faculty of Science, Cairo University, Giza 12613, EgyptThe theory of solitary waves or solitons is crucial in nonlinear models due to their ability to propagate without distortion, making them essential in fields like physics, biology, engineering, and mathematics. This study explores solitary waves in the time fractional Clannish Random Walker's Parabolic equation using two effective approaches: polynomial expansion technique (PET) and unified technique (UT). This model is particularly significant in areas such as ecology, sociology, and urban planning, where understanding individual interactions within spatial contexts is vital. By solving this equation, we gain insights into group formation and navigation, enhancing our comprehension of emergent patterns and system design. The application of PET and UT allows us to derive various solutions, including exponential, hyperbolic, and trigonometric forms. Utilizing the Maple programming language, we visualize novel phenomena, such as kink waves, anti-kink waves, and periodic lump waves. This research demonstrates that the proposed methodologies can yield precise soliton solutions, contributing valuable insights to nonlinear science and engineering applications.http://www.sciencedirect.com/science/article/pii/S2666818124003978Polynomial expansion techniqueUnified techniqueClannish Random Walker's Parabolic equationEcological and sociological perspectiveUrban planning, and materials science |
| spellingShingle | Mohammed Kbiri Alaoui Mahtab Uddin Md. Mamunur Roshid Harun Or Roshid M.S. Osman Modulation instability, and dynamical behavior of solitary wave solution of time M- fractional clannish random Walker's Parabolic equation via two analytic techniques Partial Differential Equations in Applied Mathematics Polynomial expansion technique Unified technique Clannish Random Walker's Parabolic equation Ecological and sociological perspective Urban planning, and materials science |
| title | Modulation instability, and dynamical behavior of solitary wave solution of time M- fractional clannish random Walker's Parabolic equation via two analytic techniques |
| title_full | Modulation instability, and dynamical behavior of solitary wave solution of time M- fractional clannish random Walker's Parabolic equation via two analytic techniques |
| title_fullStr | Modulation instability, and dynamical behavior of solitary wave solution of time M- fractional clannish random Walker's Parabolic equation via two analytic techniques |
| title_full_unstemmed | Modulation instability, and dynamical behavior of solitary wave solution of time M- fractional clannish random Walker's Parabolic equation via two analytic techniques |
| title_short | Modulation instability, and dynamical behavior of solitary wave solution of time M- fractional clannish random Walker's Parabolic equation via two analytic techniques |
| title_sort | modulation instability and dynamical behavior of solitary wave solution of time m fractional clannish random walker s parabolic equation via two analytic techniques |
| topic | Polynomial expansion technique Unified technique Clannish Random Walker's Parabolic equation Ecological and sociological perspective Urban planning, and materials science |
| url | http://www.sciencedirect.com/science/article/pii/S2666818124003978 |
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