Novel solitonic structure, Hamiltonian dynamics and lie symmetry algebra of biofilm

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dc.contributor.authorAsghar, Umair
dc.contributor.authorAsjad, Muhammad Imran
dc.contributor.authorFaridi, Waqas Ali
dc.contributor.authorAkgül, Ali
dc.date.accessioned2024-12-24T19:10:21Z
dc.date.available2024-12-24T19:10:21Z
dc.date.issued2024
dc.departmentSiirt Üniversitesi
dc.description.abstractIn this study, the Lie point symmetries and optimal system have been established. We discuss the biofilm model's soliton solutions. To examine a nonlinear dynamical biofilm system, which is simply a bistable Allen–Cahn equation with quartic potential, to determine solitary wave profiles using the considered equation, a new auxiliary equation technique is used. A suitable variable transformation is used to convert the governing equation into a nonlinear ordinary differential equation. The unified approach is utilized to evaluate periodic solutions, solitary and soliton solutions as well as several newly discovered exact solitary wave solutions, it can be accomplished via Mathematica (https://www.wolfram.com/mathematica/online/). The new auxiliary equation approach is an efficient method for creating unique wave profiles based on a variety of soliton families. Also, the results are graphically visualized, by using the appropriate parametric settings. The outcomes are shown graphically in two dimensions, three dimensions, and contour form. The Hamiltonian conditions are satisfied by the planer dynamical framework of equations to ensure as the system that was generated is a conservative Hamiltonian dynamical system which includes all traveling wave structures. A sensitivity evaluation is used to explore the governing model's thoroughly dynamical properties. It is demonstrated that the model becomes more dependent on the beginning conditions than the variables. The strategy could be used to look for exact solutions to various nonlinear evolution equations. We believe that this study will have important applications in different areas of science. © 2024 The Author(s)
dc.identifier.doi10.1016/j.padiff.2024.100653
dc.identifier.issn2666-8181
dc.identifier.scopus2-s2.0-85186731424
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org10.1016/j.padiff.2024.100653
dc.identifier.urihttps://hdl.handle.net/20.500.12604/4068
dc.identifier.volume9
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherElsevier B.V.
dc.relation.ispartofPartial Differential Equations in Applied Mathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_20241222
dc.subjectAllen–Cahn equation
dc.subjectHamiltonian function
dc.subjectLie symmetry analysis
dc.subjectNew auxiliary equation method
dc.subjectOptimal system
dc.subjectSensitive assessment
dc.subjectSoliton solutions
dc.titleNovel solitonic structure, Hamiltonian dynamics and lie symmetry algebra of biofilm
dc.typeArticle

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