Impressive and accurate solutions to the generalized Fokas-Lenells model
DOI:
https://doi.org/10.31349/RevMexFis.68.020701Keywords:
The perturbed complex Fokas-Lenells model, the modified simple equation method, the Riccati-Bernoulli Sub-ODE method, the travelling wave solutionsAbstract
In this article, we utilize the generalized full nonlinearity perturbed complex Fokas-Lenells model (GFLM) which is a general dynamics representation of modern electronic communications "Internet blogs, Facebook communication and Twitter comments". The modified simple equation method (MSEM) has been applied effectively to generate closed form solution. On the other hand, the Riccati-Bernoulli Sub-ODE method (RPSOM) which reduces the steps of calculation has been applied perfectly to achieve accurate solution to this equation. We established the solutions achieved by these distinct manners in same vein and parallel.
References
A. Bekir, Application of the (G’/G)-expansion method for nonlinear evolution equations, Phys. Lett. A 372 (2008) 3400,
https://doi.org/10.1016/j.physleta.2008.01.057.
E. H. M. Zahran and M. M. A. Khater, Exact traveling wave solutions for the system of shallow water wave equations and
modified Liouville equation using extended Jacobian elliptic function expansion method. American Journal of Computational
Mathematics, 4 (2014) 455, https://doi.org/10.4236/ajcm.2014.45038.
A. M. Wazwaz, Construction of soliton solutions and periodic solutions of the Boussinesq equation by the modified
decomposition method, Chaos Solitons & Fractals, 12 (2001) 1549. https://doi.org/10.1016/S0960-0779(00)00133-8.
M. S. M. Shehata, H. Rezazadeh, E H. M. Zahran, E. Tala-Tebue, and A. Bekir, New Optical Soliton Solutions of the Perturbed Fokas-Lenells Equation, Commun. Theor. Phys. 71 (2019) 1275. https://doi.org/10.1088/0253-6102/71/11/1275.
M. M. A. Khater, D. Lu, and E. H. M. Zahran, Solitary wave solutions of the Benjamin-Bona-Mahoney-Burgers equation with
dual power-law nonlinearity. Appl. Math. Inf. Sci, 11 (2017) 1, http://dx.doi.org/10.18576/amis/paper.
X.-F. Yang, Z.-C. Deng, and Y. Wei, A Riccati-Bernoulli sub-ODE method for nonlinear partial differential equations and its application. Advances in Difference Equations, 2015 (2015) 117. https://doi.org/10.1186/s13662-015-0452-4.
M. M. A. Khater, E. H. M. Zahran, and M. S. M. Shehata, Solitary wave solution of the generalized Hirota-Satsuma coupled KdV system, Journal of Egyptian Mathematical Society, 25 (2017) 8, https://doi.org/10.1016/j.joems.2016.04.006.
M. S. M. Shehata, The exp-Method and its Applications for Solving Some Nonlinear Evolution Equations in Mathematical
Physics. American Journal of Computational Mathematics 5 (2015) 468, http://dx.doi.org/10.4236/ajcm.2015.54041.
E. H. M. Zahran, TravelingWave Solutions of Nonlinear Evolution Equations via Modified exp-Expansion Method. Journal of
Computational and Theoretical Nanoscience, 12 (2015) 5716, https://doi.org/10.1166/jctn.2015.4707.
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 , 165 (2018) 102, https://doi.org/10.1016/j.ijleo.2018.03.102
M. Eslami, and M. Mirzazadeh, First integral method to look for exact solutions of a variety of Boussinesq-like equations.
Ocean Engineering, 83 (2014) 133, https://doi.org/10.1016/j.oceaneng.2014.02.026
D. Kumar, A. R. Seadawy, and A. K. Joardare, Modified Kudryashov method via new exact solutions for some conformable
fractional differential equations arising in mathematical biology, Chinese Journal of Physics, 56 (2018) 75, https://doi.org/10.1016/j.cjph.2017.11.020g.
A. Biswas, 1-soliton solution of the K(m,n) equation with generalized evolution. Phys. Lett. A 372 (2008) 4601, https://doi.org/10.1016/j.physleta.2008.05.002
H. Triki and A.M. Wazwaz, Bright and dark soliton solutions for a K(m, n) equation with t-dependent coefficients . Phys. Lett. A, 373 (2009) 2162. https://doi.org/10.1016/j.physleta.2009.04.029.
A. G Davodi, D. D Ganji, A. G Davodi, and A. Asgari, Finding general and explicit solutions (2+ 1) dimensional Broer-Kaup-Kupershmidt system nonlinear equation by exp-function method, Applied Mathematics and computation, 217 (2010) 1415. https://doi.org/10.1016/j.amc.2009.05.069.
G. Domairry, A. G. Davodi, and A. G. Davodi, Solutions for the double Sine-Gordon equation by Exp-function, Tanh, and
extended Tanh methods, Numerical Methods for Partial Differential Equations 26 (2010) 384. https://doi.org/10.1002/num.20440.
M. M. Alipour, G. Domairry, and A. G. Davodi, An application of exp-function method to approximate general and explicit
solutions for nonlinear Schr¨odinger equations, Numerical Methods for Partial Differential Equations, 27 (2011) 1016,
https://doi.org/10.1002/num.20566.
A. Asgari, D. D. Ganji, and A.G. Davodi, Extended tanh method and exp-function method and its application to (2+ 1)-
dimensional dispersive long wave nonlinear equations, Journal of the Applied Mathematics, Statistics and Informatics, 6
(2010) 61.
A. Biswas, M. Ekici, A. Sonmezoglu, and R. T. Alqahtani, Optical soliton perturbation with full nonlinearity for Fokas-Lenells equation. Optik, 165 (2018) 29, https://doi.org/10.1016/j.ijleo.2018.03.094.
A. Biswas et al., Optical solitons with differential group delay for coupled Fokas-Lenells equation using two integration
schemes. Optik, 165 (2018) 74, https://doi.org/10.1016/j.ijleo.2018.03.100
A Biswas et al., Optical soliton perturbation with Fokas-Lenells equation using three exotic and efficient integration schemes.
Optik, 165 (2018) 288, https://doi.org/10.1016/j.ijleo.2018.03.132.
A.J.M. Jawad, A. Biswas, Q. Zhou, S.P. Moshokoa, and M. Belic, Optical soliton perturbation of Fokas-Lenells equation with two integration schemes. Optik 165 (2018) 111, https://doi.org/10.1016/j.ijleo.2018.03.104.
A.-M. Wazwaz, Bright and dark soliton solutions for a k(m, n) equation with t-dependent coefficients. Phys. Lett. A, 373 (2009) 2162.
A.-M. Wazwaz, Gaussian solitary wave solutions for nonlinear evolution equations with logarithmic nonlinearities. Nonlinear
Dyn. 83 (2016) 591, https://doi.org/10.1007/s11071-015-2349-x
A. Bansal, A. H. Kara, A. Biswas, S. P. Moshokoa, and M. Belic, Optical soliton perturbation, group invariants and conservation
laws of perturbed Fokas-Lenells equation, Chaos. Solitons and Fractals 114 (2018) 275. https://doi.org/10.1016/j.chaos.2018.06.030
B. Ghanbari and J. F G Aguilar, The generalized exponential rational function method for Radhakrishnan-Kundu-Lakshmanan equation with beta-conformable time derivative, Rev. Mex. Fis 65 (2019) 503, https://doi.org/10.31349/revmexfis.65.503.
M. Senol, New Analytical Solutions of Fractional Symmetric Regularized-Long-Wave Equation, Rev. Mex. Fis. 66 (2020) 297, https://doi.org/10.31349/revmexfis.66.297
A. Cevikel and E. Aksoy, Soliton solutions of nonlinear fractional differential equations with its applications in mathematical
physics, Rev. Mex. Fis. 67 (2021) 422, http://dx.doi.org/10.31349/RevMexFis.67.422
S. Abbagari, A. Houwe, H. Rezazadeh, A. Bekir, and S. Y. Doka, Solitary wave solutions in two-core optical fibers with coupling-coefficient dispersion and Kerr nonlinearity, Rev. Mex. Fis. 67 (2021) 369, http://dx.doi.org/10.31349/RevMexFis.67.369.
Y. Gurefe, The generalized Kudryashov method for the nonlinear fractional partial differential equations with the betaderivative, Rev. Mex. Fis. 66 (2020) 771, https://doi.org/10.31349/RevMexFis.66.771.
M.A. Khan and A. Atangana, Modeling the dynamics of novel coronavirus (2019-nCov) with fractional derivative, Alexandria
Engineering Journal, 59 (2020) 2379, https://doi.org/10.1016/j.aej.2020.02.033.
M.A. Khan, Z. Hammouch, and D. Baleanu, Modeling the dynamics of hepatitis E via the Caputo-Fabrizio derivative, Math.
Model. Nat. Phenom. 14 (2019) 311. https://doi.org/10.1051/mmnp/2018074.Rev. Mex.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2022 Ahmet Bekir, E. H. M. Zahran, A. A. Gholami Davodi
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.