Keywords
Fokas-Lenells equation
(m 1/G')- Expansion Method
How to Cite
Abstract
In this research paper, we investigate some novel soliton solutions to the perturbed Fokas-Lenells equation by using the (m + 1/G') expansion method. Some new solutions are obtained and they are plotted in two and three dimensions. This technique appears as a suitable, applicable, and efficient method to search for the exact solutions of nonlinear partial differential equations in a wide range. All gained optical soliton solutions are substituted into the FokasLenells equation and they verify it. The constraint conditions are also given.
References
T. Aktürk, Y. Gürefe, and H. Bulut, “New function method to the (n+1)-dimensional nonlinear problems,” An Int. J. Optim. Control Theor. Appl., 2017. https://doi.org/10.11121/ijocta.01.2017.00489
O. A. Ilhan, A. Esen, H. Bulut, and H. M. Baskonus, “Singular solitons in the pseudo-parabolic model arising in nonlinear surface waves,” Results Phys., 2019. https://doi.org/10.1016/j.rinp.2019.01.059
S. Arshed et al., “Optical solitons pertutabation with FokasLenells equation by exp(−ϕ(ξ))-expansion method,” Optik (Stuttg)., 2019. https://doi.org/10.1016/j.ijleo.2018.10.136
A. Biswas, M. Ekici, A. Sonmezoglu, and R. T. Alqahtani, “Optical soliton perturbation with full nonlinearity for Fokas– Lenells equation,” Optik (Stuttg)., 2018. https://doi.org/10.1016/j.ijleo.2018.03.094
A. Biswas, M. Ekici, A. Sonmezoglu, and R. T. Alqahtani, “Optical solitons with differential group delay for coupled Fokas–Lenells equation by extended trial function scheme,” Optik (Stuttg)., 2018. https://doi.org/10.1016/j.ijleo.2018.03.102
L. Ling, B. F. Feng, and Z. Zhu, “General soliton solutions to a coupled Fokas–Lenells equation,” Nonlinear Anal. Real World Appl., 2018. https://doi.org/10.1016/j.nonrwa.2017.08.013
H. Triki and A. M. Wazwaz, “Combined optical solitary waves of the Fokas—Lenells equation,” Waves in Random and Complex Media, 2017. https://doi.org/10.1080/17455030.2017.1285449
Y. Zhang, J. W. Yang, K. W. Chow, and C. F. Wu, “Solitons, breathers and rogue waves for the coupled Fokas–Lenells system via Darboux transformation,” Nonlinear Anal. Real World Appl., 2017. https://doi.org/10.1016/j.nonrwa.2016.06.006
A. Biswas et al., “Optical soliton perturbation with Fokas– Lenells equation using three exotic and efficient integration schemes,” Optik (Stuttg)., 2018. https://doi.org/10.1016/j.ijleo.2018.03.132
E. V. Krishnan, A. Biswas, Q. Zhou, and M. Alfiras, “Optical soliton perturbation with Fokas–Lenells equation by mapping methods,” Optik (Stuttg)., 2019. https://doi.org/10.1016/j.ijleo.2018.10.017
H. S. Shukla, M. Tamsir, and V. K. Srivastava, “Numerical simulation of two dimensional sine-Gordon solitons using modified cubic B-spline differential quadrature method,” AIP Adv., 2015. https://doi.org/10.1063/1.4906256
G. Yel, H. M. Baskonus, and H. Bulut, “Novel archetypes of new coupled Konno–Oono equation by using sine–Gordon expansion method,” Opt. Quantum Electron., 2017. https://doi.org/10.1007/s11082-017-1127-z
H. M. Baskonus and H. Bulut, “New complex exact travelling wave solutions for the generalized-Zakharov equation with complex structures,” An Int. J. Optim. Control Theor. Appl., 2016. https://doi.org/10.11121/ijocta.01.2016.00295
H. Triki and A. M. Wazwaz, “New types of chirped soliton solutions for the Fokas-Lenells equation,” in International Journal of Numerical Methods for Heat and Fluid Flow, 2017. https://doi.org/10.1016/j.cnsns.2016.06.026
J. He, S. Xu, and K. Porsezian, “Rogue waves of the fokaslenells equation,” J. Phys. Soc. Japan, 2012. https://doi.org/10.1143/JPSJ.81.124007
Durur, H., Ilhan, E., & Bulut, H. (2020). Novel Complex Wave Solutions of the (2+ 1)- Dimensional Hyperbolic Nonlinear Schrödinger Equation. Fractal and Fractional, 4(3), 41. https://doi.org/10.3390/fractalfract4030041
Yokus, A., Durur, H., Ahmad, H., & Yao, S. W. (2020). Construction of Different Types Analytic Solutions for the Zhiber-Shabat Equation. Mathematics, 8(6), 908. https://doi.org/10.3390/math8060908
Durur, H. (2020). Different types analytic solutions of the (1+ 1)-dimensional resonant nonlinear Schrödinger’s equation using (G′/G)-expansion method. Modern Physics Letters B, 34(03), 2050036. https://doi.org/10.1142/S0217984920500360
Yokus, A., Durur, H., & Ahmad, H. (2020). Hyperbolic type solutions for the couple Boiti-Leon-Pempinelli system. FactaUniversitatis, Series: Mathematics and Informatics, 35(2), 523-531.
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Copyright (c) 2020 Bulut, Hasan, Khalid, Ban Jamal