Lie symmetries, bifurcation analysis, and Jacobi elliptic function solutions to the nonlinear Kodama equation

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dc.authoridAlizadeh, Farzaneh/0000-0002-1851-0397
dc.authoridHosseini, Kamyar/0000-0001-7137-1456
dc.authoridHassan, Ahmed/0000-0002-1369-326X
dc.contributor.authorHosseini, K.
dc.contributor.authorAlizadeh, F.
dc.contributor.authorHincal, E.
dc.contributor.authorBaleanu, D.
dc.contributor.authorAkgul, A.
dc.contributor.authorHassan, A. M.
dc.date.accessioned2024-12-24T19:27:43Z
dc.date.available2024-12-24T19:27:43Z
dc.date.issued2023
dc.departmentSiirt Üniversitesi
dc.description.abstractThe present article formally studies the propagation of optical pulses in a nonlinear medium governed by the nonlinear Kodama equation. For this purpose, the Lie symmetries group is first adopted for similarity reduction and constructing some exact solutions of the governing equation. After deriving the dynamical system of the nonlinear Kodama equation, its bifurcation analysis is accomplished using the idea of the planar dynamical system. Through perturbing the resultant dynamical system using a trigonometric function, chaotic characteristics of the governing model are analyzed by serving several two- and three-dimensional phase portraits. A sensitivity analysis of the dynamical system is performed using the Runge-Kutta method to ensure that small changes in initial conditions have little impact on solution stability. Finally, using the technique of the planar dynamical system, a number of Jacobi elliptic function solutions (in special cases, bright and dark solitons) are constructed for the nonlinear Kodama equation. It has been shown that bright and dark solitons can be controlled for their width and height effectively by the achievements of the current paper.
dc.identifier.doi10.1016/j.rinp.2023.107129
dc.identifier.issn2211-3797
dc.identifier.scopus2-s2.0-85175379237
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.1016/j.rinp.2023.107129
dc.identifier.urihttps://hdl.handle.net/20.500.12604/6760
dc.identifier.volume54
dc.identifier.wosWOS:001108793700001
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherElsevier
dc.relation.ispartofResults in Physics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241222
dc.subjectNonlinear Kodama equation
dc.subjectLie symmetries
dc.subjectBifurcation analysis
dc.subjectChaotic characteristics
dc.subjectSensitivity analysis
dc.subjectBright and dark solitons
dc.titleLie symmetries, bifurcation analysis, and Jacobi elliptic function solutions to the nonlinear Kodama equation
dc.typeArticle

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