Perturbed soliton solutions for an integral modified KdV equation
•An integral modified KdV equation is considered.•The KdV equation is solved for the solitons solutions using perturbation technique.•The effect of inhomogeneity is studied and show deformed soliton excitation. We investigate throughout this paper the effect of inhomogeneity on the propagation of so...
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| Veröffentlicht in: | Communications in nonlinear science & numerical simulation Jg. 91; S. 105437 |
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| Abstract | •An integral modified KdV equation is considered.•The KdV equation is solved for the solitons solutions using perturbation technique.•The effect of inhomogeneity is studied and show deformed soliton excitation.
We investigate throughout this paper the effect of inhomogeneity on the propagation of solitons in ferromagnetic systems governing the magnetization evolution in a magnetic medium. Indeed we focus our attention on a nonlinear evolution equation derived by M. Saravanan and A. Arnaudon (2018 Phys. Lett. A 382 2638) that takes into account the inhomogeneity we are interested in. The perturbed soliton solutions are constructed using a multiple scale soliton perturbation theory by solving the associated linear eigenvalue problem with proper derivation of complete set of eigenfunctions. We present two types of inhomogeneities, such as localized and linear, and their effects on soliton propagation. It is found that the localized inhomogeneity supports stable soliton excitations with constant amplitude. |
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| AbstractList | We investigate throughout this paper the effect of inhomogeneity on the propagation of solitons in ferromagnetic systems governing the magnetization evolution in a magnetic medium. Indeed we focus our attention on a nonlinear evolution equation derived by M. Saravanan and A. Arnaudon (2018 Phys. Lett. A 382 2638) that takes into account the inhomogeneity we are interested in. The perturbed soliton solutions are constructed using a multiple scale soliton perturbation theory by solving the associated linear eigenvalue problem with proper derivation of complete set of eigenfunctions. We present two types of inhomogeneities, such as localized and linear, and their effects on soliton propagation. It is found that the localized inhomogeneity supports stable soliton excitations with constant amplitude. •An integral modified KdV equation is considered.•The KdV equation is solved for the solitons solutions using perturbation technique.•The effect of inhomogeneity is studied and show deformed soliton excitation. We investigate throughout this paper the effect of inhomogeneity on the propagation of solitons in ferromagnetic systems governing the magnetization evolution in a magnetic medium. Indeed we focus our attention on a nonlinear evolution equation derived by M. Saravanan and A. Arnaudon (2018 Phys. Lett. A 382 2638) that takes into account the inhomogeneity we are interested in. The perturbed soliton solutions are constructed using a multiple scale soliton perturbation theory by solving the associated linear eigenvalue problem with proper derivation of complete set of eigenfunctions. We present two types of inhomogeneities, such as localized and linear, and their effects on soliton propagation. It is found that the localized inhomogeneity supports stable soliton excitations with constant amplitude. |
| ArticleNumber | 105437 |
| Author | Saravanan, M. Herman, Russell L. |
| Author_xml | – sequence: 1 givenname: M. surname: Saravanan fullname: Saravanan, M. email: saravanan_manickam@yahoo.com, saravanm4@srmist.edu.in organization: Department of Physics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Ramapuram Campus, Ramapuram, Chennai - 600 089, Tamilnadu, India – sequence: 2 givenname: Russell L. surname: Herman fullname: Herman, Russell L. organization: Department of Mathematics and Statistics, University of North Carolina Wilmington, Wilmington, NC 28403, USA |
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| Cites_doi | 10.1103/PhysRevE.54.6816 10.1016/j.physd.2007.04.005 10.1103/PhysRevLett.15.240 10.1088/0953-8984/7/23/022 10.1088/0305-4470/37/17/007 10.1016/j.physleta.2018.07.015 10.1088/0022-3719/15/36/007 10.1103/PhysRevLett.90.227601 10.1016/j.aop.2014.10.003 10.1016/j.cnsns.2018.09.021 10.1103/PhysRevB.53.R2930 10.1088/0305-4470/23/12/017 10.1103/PhysRevB.66.184433 10.1063/1.1664700 10.1088/0305-4470/36/42/005 10.1103/PhysRevB.77.144416 10.1098/rspa.1978.0110 10.1016/0375-9601(77)90727-7 10.1016/j.jmmm.2019.03.058 10.1016/j.chaos.2008.07.033 10.1103/PhysRevE.58.1064 10.1103/PhysRevLett.17.996 10.1002/sapm197757113 10.1088/1751-8113/41/18/185201 10.1103/PhysRevB.77.224416 10.1002/sapm1981643225 10.1088/1751-8113/43/12/125201 10.1103/PhysRevE.84.031928 |
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| Snippet | •An integral modified KdV equation is considered.•The KdV equation is solved for the solitons solutions using perturbation technique.•The effect of... We investigate throughout this paper the effect of inhomogeneity on the propagation of solitons in ferromagnetic systems governing the magnetization evolution... |
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| SubjectTerms | Eigenvalues Eigenvectors Ferromagnetism Inhomogeneity Integral equations Korteweg-Devries equation Nonlinear equations Nonlinear evolution equations Perturbation theory Propagation Solitary waves |
| Title | Perturbed soliton solutions for an integral modified KdV equation |
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