Lie symmetry analysis and solitary wave solution of biofilm model Allen-Cahn
Abstract The investigation presented in this study delves into the analysis of Lie symmetries for the bistable Allen-Cahn (BAC) equation with a quartic potential, specifically applied to the biofilm model. By employing the Lie symmetry method, we have acquired the Lie infinitesimal generators for th...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Nature Portfolio
2024-06-01
|
| Series: | Scientific Reports |
| Subjects: | |
| Online Access: | https://doi.org/10.1038/s41598-024-62315-5 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1841559436136546304 |
|---|---|
| author | Muhammad Shakeel Naseem Abbas Muhammad Junaid U. Rehman Fehaid Salem Alshammari Abdullah Al-Yaari |
| author_facet | Muhammad Shakeel Naseem Abbas Muhammad Junaid U. Rehman Fehaid Salem Alshammari Abdullah Al-Yaari |
| author_sort | Muhammad Shakeel |
| collection | DOAJ |
| description | Abstract The investigation presented in this study delves into the analysis of Lie symmetries for the bistable Allen-Cahn (BAC) equation with a quartic potential, specifically applied to the biofilm model. By employing the Lie symmetry method, we have acquired the Lie infinitesimal generators for the considered model. Using a transformation method, the nonlinear partial differential equations (NPDEs) are converted into various nonlinear ordinary differential equations (NLODEs), providing the numerous closed-form solitary wave solutions. The obtained solutions manifest in various forms including dark, bright, kink, anti-kink, and periodic types using diverse strategies. To enhance the physical interpretation, the study presents 3D, 2D, and contour plots of the acquired solutions. Every graph’s wave-like structure contains information about the structural behaviour of the bacteria that build biofilms on surfaces where rectangles have different densities. This analysis enhances comprehension of the complex dynamics present in areas like fluid dynamics, fiber optics, biology, ocean physics, coastal engineering, and nonlinear complex physical systems. |
| format | Article |
| id | doaj-art-6c0bbd9a68d041389f6c46cf762bb012 |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2024-06-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-6c0bbd9a68d041389f6c46cf762bb0122025-01-05T12:29:05ZengNature PortfolioScientific Reports2045-23222024-06-0114111810.1038/s41598-024-62315-5Lie symmetry analysis and solitary wave solution of biofilm model Allen-CahnMuhammad Shakeel0Naseem Abbas1Muhammad Junaid U. Rehman2Fehaid Salem Alshammari3Abdullah Al-Yaari4School of Mathematics and Statistics, Central South UniversityDepartment of Mathematics, Quaid-e-Azam University 45320Department of Automation, Biomechanics, and Mechatronics, Lodz University of TechnologyDepartment of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU)Department of Mathematics, Faculty of Applied Science, Thamar UniversityAbstract The investigation presented in this study delves into the analysis of Lie symmetries for the bistable Allen-Cahn (BAC) equation with a quartic potential, specifically applied to the biofilm model. By employing the Lie symmetry method, we have acquired the Lie infinitesimal generators for the considered model. Using a transformation method, the nonlinear partial differential equations (NPDEs) are converted into various nonlinear ordinary differential equations (NLODEs), providing the numerous closed-form solitary wave solutions. The obtained solutions manifest in various forms including dark, bright, kink, anti-kink, and periodic types using diverse strategies. To enhance the physical interpretation, the study presents 3D, 2D, and contour plots of the acquired solutions. Every graph’s wave-like structure contains information about the structural behaviour of the bacteria that build biofilms on surfaces where rectangles have different densities. This analysis enhances comprehension of the complex dynamics present in areas like fluid dynamics, fiber optics, biology, ocean physics, coastal engineering, and nonlinear complex physical systems.https://doi.org/10.1038/s41598-024-62315-5Biofilm modelLie symmetry techniqueSolitory wave solution |
| spellingShingle | Muhammad Shakeel Naseem Abbas Muhammad Junaid U. Rehman Fehaid Salem Alshammari Abdullah Al-Yaari Lie symmetry analysis and solitary wave solution of biofilm model Allen-Cahn Scientific Reports Biofilm model Lie symmetry technique Solitory wave solution |
| title | Lie symmetry analysis and solitary wave solution of biofilm model Allen-Cahn |
| title_full | Lie symmetry analysis and solitary wave solution of biofilm model Allen-Cahn |
| title_fullStr | Lie symmetry analysis and solitary wave solution of biofilm model Allen-Cahn |
| title_full_unstemmed | Lie symmetry analysis and solitary wave solution of biofilm model Allen-Cahn |
| title_short | Lie symmetry analysis and solitary wave solution of biofilm model Allen-Cahn |
| title_sort | lie symmetry analysis and solitary wave solution of biofilm model allen cahn |
| topic | Biofilm model Lie symmetry technique Solitory wave solution |
| url | https://doi.org/10.1038/s41598-024-62315-5 |
| work_keys_str_mv | AT muhammadshakeel liesymmetryanalysisandsolitarywavesolutionofbiofilmmodelallencahn AT naseemabbas liesymmetryanalysisandsolitarywavesolutionofbiofilmmodelallencahn AT muhammadjunaidurehman liesymmetryanalysisandsolitarywavesolutionofbiofilmmodelallencahn AT fehaidsalemalshammari liesymmetryanalysisandsolitarywavesolutionofbiofilmmodelallencahn AT abdullahalyaari liesymmetryanalysisandsolitarywavesolutionofbiofilmmodelallencahn |