Different soliton solutions to the modified equal-width wave equation with Beta-time fractional derivative via two different methods
Keywords:MEW equation, Beta-time derivative, Extended Jacobi's elliptic expansion function method, Kudryashov method, Soliton solutions.
AbstractIn this paper, different types of soliton solutions of the modified equal width wave (MEW) equation with beta time derivative are obtained by implementing the two different methods named as: extended Jacobi's elliptic expansion function method and Kudryashov method. The dark, bright, singular and other solitons are achieved. The obtained soliton solutions are verified through MATHEMATICA. At the end, the results are also explained through graphs. These soliton solutions suggest that these two methods are effective, straight forward and reliable as compare to other methods. The obtained results can be used in describing the substantial understanding of the studious structures as well as others related non-linear physical structures.
A. Biswas and R. T. Alqahtani, Chirp-free bright optical solitons for perturbed Gerdjikov-Ivanov equation by semi-inverse
variational principle, Optik 147 (2017) 72, https://doi.org/10.1016/j.ijleo.2017.08.019.
A. Bekir, Applications of the extended tanh method for coupled nonlinear evolution equations, Commun. Nonlinear Sci. Numer.
Simul. 13 (2008) 1748, https://doi.org/10.1016/j.cnsns.2007.05.001.
H. Rezazadeh et al., Hyperbolic rational solutions to a variety of conformable fractional Boussinesq-like equations, Nonlinear Eng. 8 (2019) 224, https://doi.org/10.1515/nleng-2018-0033.
J.-H. He, Variational principle and periodic solution of the Kundu-Mukherjee-Naskar equation, Res. Phys. 17 (2020) 103031, https://doi.org/10.1016/j.rinp.2020.103031.
Y. Yıldırım, and M. Mirzazadeh, Optical pulses with KunduMukherjee-Naskar model in fiber communication systems, Chin. J. Phys. 64 (2020) 183, https://doi.org/10.1016/j.cjph.2019.10.025.
B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, Spatiotemporal optical solitons, J. Opt. B 7 (2005) R53, https://doi.org/10.1088/1464-4266/7/5/R02.
A. Zafar, M. Raheel, and A. Bekir, Exploring the dark and singular soliton solutions of Biswas-Arshed model with full nonlinear form, Optik 204 (2020) 164133, https://doi.org/10.1016/j.ijleo.2019.164133.
W. Malfliet, Solitary wave solutions of nonlinear wave equations, Am. J. Phys. 60 (1992) 650, https://doi.org/10.1119/1.17120.
K. R. Raslan, K. K. Ali, and M. A. Shallal, The modified extended tanh method with the Riccati equation for solving the space-time fractional EW and MEW equations, Chaos Solitons Fractals 103 (2017) 404, https://doi.org/10.1016/j.chaos.2017.06.029.
D. Shi and Y. Zhang, Diversity of exact solutions to the conformable space-time fractional MEW equation, Appl. Math.Lett. 99 (2020) 105994, https://doi.org/10.1016/j.aml.2019.07.025.
A. Biswas, M. Ekici, A. Sonmezoglu, and M. R. Belic, Highly dispersive optical solitons with cubic-quintic-septic law by extended Jacobi’s elliptic function expansion, Optik 183 (2019) 571, https://doi.org/10.1016/j.ijleo.2019.02.127.
A. Biswas, M. Ekici, A. Sonmezoglu, and M. R. Belic, Highly dispersive optical solitons with Kerr law nonlinearity by extended Jacobi’s elliptic function expansion, Optik 183 (2019) 395, https://doi.org/10.1016/j.ijleo.2019.02.050.
M. A. Abdou and A. Elhanbaly, Construction of periodic and solitary wave solutions by the extended Jacobi elliptic function expansion method, Commun. Nonlinear Sci. Numer. Simul. 12 (2007) 1229, https://doi.org/10.1016/j.cnsns.2006.01.013.
H. Zhang, Extended Jacobi elliptic function expansion method and its applications, Commun. Nonlinear Sci. Numer. Simul. 12
(2007) 627, https://doi.org/10.1016/j.cnsns.2005.08.003.
W. Zhang, Extended Jacobi Elliptic Function Expansion Method to the ZK-MEW Equation, Int. J. Differ. Equ. 2011 (2011) 451420, https://doi.org/10.1155/2011/451420.
R. I. Nuruddeen and A. M. Nass, Exact solitary wave solution for the fractional and classical GEW-Burgers equations: an application of Kudryashov method, J. Taibah Univ. Sci. 12 (2018) 309, https://doi.org/10.1080/16583655.2018.1469283.
K. Hosseini, M. Mirzazadeh, M. Ilie, and S. Radmehr, Dynamics of optical solitons in the perturbed Gerdjikov-Ivanov equation, Optik 206 (2020) 164350, https://doi.org/10.1016/j.ijleo.2020.164350.
K. Hosseini, and Z. Ayati, Exact solutions of space-time fractional EW and modified EW equations using Kudryashov method, Nonlinear Sci. Lett. A 7 (2016) 58.
N. A. Kudryashov, Method for finding highly dispersive optical solitons of nonlinear differential equations, Optik 206 (2020) 163550, https://doi.org/10.1016/j.ijleo.2019.163550.
K. Hosseini, M. Mirzazadeh, M. Ilie, and J. F. Gomez-Aguilar, ´Biswas-Arshed equation with the beta time derivative: Optical solitons and other solutions, Optik 217 (2020) 164801, https://doi.org/10.1016/j.ijleo.2020.164801.
K. Hosseini, M. Mirzazadeh, and J. F. Gomez-Aguilar, ´Soliton solutions of the Sasa-Satsuma equation in the monomode optical fibers including the beta-derivatives, Optik 224 (2020) 165425, https://doi.org/10.1016/j.ijleo.2020.165425.
H. Yepes-Martínez, J. F. Gomez-Aguilar, and D. Baleanu, ´Beta-derivative and subequation method applied to the optical solitons in medium with parabolic law nonlinearity and higher order dispersion, Optik 155 (2018) 357, https://doi.org/10.1016/j.ijleo.2017.10.104.
H. Yepez-Martínez and J. F. Gomez-Aguilar, Fractional subequation method for Hirota-Satsuma-coupled KdV equation and coupled mKdV equation using the Atangana’s conformable derivative, Waves Random Complex Media 29 (2019) 678, https://doi.org/10.1080/17455030.2018.1464233.
H. Yepez-Martínez and J. F. Gomez-Aguilar, Optical solitons solution of resonance nonlinear Schrodinger type equation with Atangana’s-conformable derivative using subequation method, Waves Random Complex Media 31 (2021) 573, https://doi.org/10.1080/17455030.2019.1603413.
A. Atangana, D. Baleanu and A. Alsaedi, Analysis of timefractional Hunter-Saxton equation: a model of neumatic liquid crystal, Open Phys. 14 (2016) 145, https://doi.org/10.1515/phys-2016-0010.
A. Atangana and R. T. Alqahtani, Modelling the Spread of River Blindness Disease via the Caputo Fractional Derivative and the Beta-derivative, Entropy 18 (2016) 40, https://doi.org/10.3390/e18020040.
H. Yepez-Martínez, J.F. Gomez-Aguilar and D. Baleanu, Beta-derivative and sub-equation method applied to the optical solitons in medium with parabolic law nonlinearity and higher order dispersion, Optik. 155 (2018) 357.
A. Yusuf, M. Inc, A. I. Aliyu, and D. Baleanu, Optical Solitons Possessing Beta Derivative of the Chen-Lee-Liu Equation in Optical Fibers, Front. Phys. 7 (2019) 34, https://doi.org/10.3389/fphy.2019.00034.
M. F. Uddin, M. Golam Hafez, Z. Hammouch, and D. Baleanu, Periodic and rogue waves for Heisenberg models of ferromagnetic spin chains with fractional beta derivative evolution and obliqueness, Waves Random Complex Media (in press), https://doi.org/10.1080/17455030.2020.1722331.
B. Ghanbari and J. F. Gomez-Aguilar, The generalized exponential rational function method for Radhakrishnan-KunduLakshmanan equation with β-conformable time derivative, Rev.Mex. Fis. 65 (2019) 503, https://doi.org/10.31349/RevMexFis.65.503.
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