Lie symmetries, bifurcation analysis, and Jacobi elliptic function solutions to the nonlinear Kodama equation
The 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...
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2023-11-01
|
| Series: | Results in Physics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379723009221 |
| _version_ | 1797615963649081344 |
|---|---|
| author | K. Hosseini F. Alizadeh E. Hinçal D. Baleanu A. Akgül A.M. Hassan |
| author_facet | K. Hosseini F. Alizadeh E. Hinçal D. Baleanu A. Akgül A.M. Hassan |
| author_sort | K. Hosseini |
| collection | DOAJ |
| description | The 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. |
| first_indexed | 2024-03-11T07:34:29Z |
| format | Article |
| id | doaj.art-f6f4e898d43b46c090a3cc1f7e2a95de |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-03-11T07:34:29Z |
| publishDate | 2023-11-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-f6f4e898d43b46c090a3cc1f7e2a95de2023-11-17T05:26:38ZengElsevierResults in Physics2211-37972023-11-0154107129Lie symmetries, bifurcation analysis, and Jacobi elliptic function solutions to the nonlinear Kodama equationK. Hosseini0F. Alizadeh1E. Hinçal2D. Baleanu3A. Akgül4A.M. Hassan5Department of Mathematics, Near East University TRNC, Mersin 10, Turkey; Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon; Corresponding authors at: Department of Mathematics, Near East University TRNC, Mersin 10, Turkey (K. Hosseini).Department of Mathematics, Near East University TRNC, Mersin 10, TurkeyDepartment of Mathematics, Near East University TRNC, Mersin 10, TurkeyDepartment of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon; Institute of Space Sciences, Magurele-Bucharest, Romania; Corresponding authors at: Department of Mathematics, Near East University TRNC, Mersin 10, Turkey (K. Hosseini).Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon; Siirt University, Art and Science Faculty, Department of Mathematics, 56100 Siirt, Turkey; Near East University, Mathematics Research Center, Department of Mathematics, Near East Boulevard, PC: 99138, Nicosia /Mersin 10, TurkeyFaculty of Engineering, Future University in Egypt, New Cairo 11835, EgyptThe 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.http://www.sciencedirect.com/science/article/pii/S2211379723009221Nonlinear Kodama equationLie symmetriesBifurcation analysisChaotic characteristicsSensitivity analysisBright and dark solitons |
| spellingShingle | K. Hosseini F. Alizadeh E. Hinçal D. Baleanu A. Akgül A.M. Hassan Lie symmetries, bifurcation analysis, and Jacobi elliptic function solutions to the nonlinear Kodama equation Results in Physics Nonlinear Kodama equation Lie symmetries Bifurcation analysis Chaotic characteristics Sensitivity analysis Bright and dark solitons |
| title | Lie symmetries, bifurcation analysis, and Jacobi elliptic function solutions to the nonlinear Kodama equation |
| title_full | Lie symmetries, bifurcation analysis, and Jacobi elliptic function solutions to the nonlinear Kodama equation |
| title_fullStr | Lie symmetries, bifurcation analysis, and Jacobi elliptic function solutions to the nonlinear Kodama equation |
| title_full_unstemmed | Lie symmetries, bifurcation analysis, and Jacobi elliptic function solutions to the nonlinear Kodama equation |
| title_short | Lie symmetries, bifurcation analysis, and Jacobi elliptic function solutions to the nonlinear Kodama equation |
| title_sort | lie symmetries bifurcation analysis and jacobi elliptic function solutions to the nonlinear kodama equation |
| topic | Nonlinear Kodama equation Lie symmetries Bifurcation analysis Chaotic characteristics Sensitivity analysis Bright and dark solitons |
| url | http://www.sciencedirect.com/science/article/pii/S2211379723009221 |
| work_keys_str_mv | AT khosseini liesymmetriesbifurcationanalysisandjacobiellipticfunctionsolutionstothenonlinearkodamaequation AT falizadeh liesymmetriesbifurcationanalysisandjacobiellipticfunctionsolutionstothenonlinearkodamaequation AT ehincal liesymmetriesbifurcationanalysisandjacobiellipticfunctionsolutionstothenonlinearkodamaequation AT dbaleanu liesymmetriesbifurcationanalysisandjacobiellipticfunctionsolutionstothenonlinearkodamaequation AT aakgul liesymmetriesbifurcationanalysisandjacobiellipticfunctionsolutionstothenonlinearkodamaequation AT amhassan liesymmetriesbifurcationanalysisandjacobiellipticfunctionsolutionstothenonlinearkodamaequation |