Soliton Solutions for space-time fractional Heisenberg ferromagnetic spin chain equation by generalized Kudryashov method and modified exp -expansion function method
DOI:
https://doi.org/10.31349/RevMexFis.67.393Keywords:
Heisenberg ferromagnetic spin chain equation, generalized Kudryashov method, modified exp -expansion function method, dark soliton, bright soliton, dark-bright soliton.Abstract
This paper addresses the Heisenberg ferromagnetic spin chain equation with beta time derivative. Integration schemes are used to study this equation. They are generalized Kudryashov method and modified exp -expansion function method. Dark, bright and dark-bright soliton solutions of this equation are procured.
References
M. A. Akbar, N. H. M. Ali, T. Tanjim, Adequate soliton solutions to the perturbed Boussinesq equation and the KdV-Caudrey-Dodd-Gibbon equation, Journal of King Saud University-Science 32 (2020) 2777–2785.
J. Chen, Q. Yan, H. Zhang, Multiple bright soliton solutions of a reverse-space nonlocal nonlinear Schrödinger equation, Applied Mathematics Letters 106 (2020) 106375, 1-7.
M. A. Kayum, S. Ara, H. K. Barman, M. A. Akbar, Soliton solutions to voltage analysis in nonlinear electrical transmission lines and electric signals in telegraph lines, Results in Physics 18 (2020) 103269,1-10.
X. Guan, W. Liu, Multiple-soliton and lump-kink solutions for a generalized (3+1)-dimensional Kadomtsev-Petviashvili equation, Results in Physics 17 (2020) 103149, 1-6.
C. K. Kuo, W. X. Ma, A study on resonant multi-soliton solutions to the (2+1)-dimensional Hirota–Satsuma–Ito equations via the linear superposition principle, Nonlinear Analysis 190 (2020) 111592, 1-9.
C. G. Böhmer, Y. Lee, P. Neff, Soliton solutions in geometrically nonlinear Cosserat micropolar elasticity with large deformations, Wave Motion 84 (2019) 110–124.
A. Biswas, S. Komar, Introduction to non-Kerr optical solitons, CRC Press, Boca Raton, FL. USA, 2006.
A. Biswas, Q. Zhou, M. Z. Ullah, M. Asma, S. P. Moshokoa, M. Belic, Perturbation theory and optical soliton cooling with anti-cubic nonlinearity, Optik 142 (2017) 73-76.
M. Savescu, A. H. Bhrawy, A. A. Alshaery, E. M. Hilal, K.R. Khan, M. F. Mahmood, A. Biswas,Optical solitons in nonlinear directional couplers with spatio-temporal dispersion, Journal Modern Optics, 61(5) (2014) 441-458.
K. Hosseini, M. Mirzazadeh, M. Ilie, J. F. Gómez-Aguilar, Biswas–Arshed equation with the beta time derivative: Optical solitons and other solutions, Optik- International Journal for Light and Electron Optics, 217 (2020) 164801, 1-7.
A. H. Arnous, A. R. Seadawy, R. T. Alqahtani, A. Biswas, Optical solitons with complex Ginzburg–Landau equation by modified simple equation method, Optik 144 (2017) 475–480.
M. Savescu, A.H. Bhrawy, A.A. Alshaery, E.M. Hilal, K. R. Khan, M.F. Mahmood, A. Biswas, Optical solitons in nonlinear directional couplers with spatio-temporal dispersion, Journal of Modern Optics, 61(5) (2014) 441-458.
H. Triki, S. Crutcher, A. Yildirim, T. Hayat, O. M. Aldossary, A. Biswas, Bright and Dark Solitons of the Modified Complex Ginzburg Landau Equation with Parabolic and Dual-Power Nonlinearity, Romanian Reports in Physics, 64(2) (2012) 367–380.
Q. Zhou, Y. Zhong, M. Mirzazadeh, A. H. Bhrawy, E. Zerrad, A. Biswas, Thirring combo-solitons with cubic nonlinearity and spatio-temporal dispersion, Waves in Random and Complex Media 26(2) (2016) 204-210.
Q. Zhou, L. Liu, H. Zhang, M. Mirzazadeh, A. H. Bhrawy, E. Zerrad, S. Moshokoa, A. Biswas, Dark and singular optical solitons with competing nonlocal nonlinearities, Optica Applicata 46(1) (2016) 79-86.
M. M. Latha, C. C. Vasanthi, An integrable model of (2+1)-dimensional Heisenberg ferromagnetic spin chain and soliton excitations, Phys. Scr. 89 (2014) 065204,1-12.
X. H. Zhao, B. Tian, D. Y. Liu, X. Y. Wu, J. Chai, Y. J. Guo, Dark solitons interaction for a (2+1)-dimensional nonlinear Schrödinger equation in the Heisenberg ferromagnetic spin chain, Superlattices and Microstructures 100 (2016) 587-595.
B. Q. Li, Y. L. Ma, Lax pair, Darboux transformation and Nth-order rogue wave solutions for a (2+1)-dimensional Heisenberg ferromagnetic spin chain equation, Computers and Mathematics with Applications 77 (2019) 514–524.
M. S. Hashemi, Some new exact solutions of (2+1)-dimensional nonlinear Heisenberg ferromagnetic spin chain with the conformable time fractional derivative, Opt Quant Electron 50(79) (2018) 1-11.
S. Tuluce Demiray, H. Bulut, Soliton solutions of some nonlinear evolution problems by GKM, Neural Comput & Applic, 31(1) (2019) 287-294.
S. Tuluce Demiray, Y.Pandir, H. Bulut, New Soliton Solutions for Sasa-Satsuma Equation, Waves in Random and Complex Media, 25(3) (2015) 417-428.
S. Tuluce Demiray, Y. Pandir, H. Bulut, New Solitary Wave Solutions of Maccari System, Ocean Engineering, 103 (2015) 153-159.
S. Tuluce Demiray, Y. Pandir, H. Bulut, All Exact Travelling Wave Solutions of Hirota Equation and Hirota-Maccari System, Optik, 127 (2016) 1848-1859.
S. Tuluce Demiray, H. Bulut, Analytical Solutions of Phi-four equations, An International Journal of Optimization and Control: Theories & Applications, 7(3) (2017) 275–280.
S. Tuluce Demiray, H. Bulut, A New Method for (4+1) Dimensional Fokas Equation, ITM Web of Conferences, 22(01065) (2018) 1–5.
S. Tuluce Demiray, H. Bulut, Hyperbolic Function Solutions for Positive Gardner-KP Equation, J. Adv. Math. Stud., 12(1) (2019) 101-106.
S. Tuluce Demiray, H. Bulut, A New Approach for Nizhnik-Novikov-Veselov System, Advanced Mathematical Models & Applications, 4(1) (2019) 79-85.
A. Atangana, D. Baleanu, A. Alsaedi, Analysis of time-fractional Hunter–Saxton equation: a model of neumatic liquid crystal, Open Phys. 14 (2016) 145–149.
M. F. Uddin, M. G. Hafez, Z. Hammouch, D. Baleanu, Periodic and rogue waves for Heisenberg models of ferromagnetic spin chains with fractional beta derivative evolution and obliqueness, Waves in Random and Complex Media, https://doi.org/10.1080/17455030.2020.1722331 (2020) 1-15.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2021 Seyma Tuluce Demiray, Ugur Bayrakci
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors retain copyright and grant the Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.