Solitary Wave Solutions for Time-Fractional Dispersive LongWave Equations via Generalized Kudryashov-Auxaliry Method
DOI:
https://doi.org/10.26713/cma.v12i3.1504Keywords:
Generalized Kudryashov method, Dispersive long wave equationsAbstract
In this paper, we present Generalized Kudryashov-Jacobian Method (GKJM) to obtain new type of general exact solutions for nonlinear partial differential equations. GKJM is applied to time-fractional dispersive long wave equations. Seven types solutions of this equation are obtained and including trigonometric function and hyperbolic function. The obtained solutions represent kink wave, anti-kink wave, singular wave, and periodic wave.
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K. Ayub, M. Y. Khan and Q. Mahmood-Ul-Hassan, Solitary and periodic wave solutions of Calogero-Bogoyavlenskii-Schiff equation via exp-function methods, Computers & Mathematics with Applications 74 (2017), 3231 – 3241, DOI: 10.1016/j.camwa.2017.08.021.
Z. Bin, (G0/G)-Expansion method for solving fractional partial differential equations in the theory of mathematical physics, Communications in Theoretical Physics 58 (2012), 623 – 630, DOI: 10.1088/0253-6102/58/5/02.
A. Biswas, A. Sonmezoglu, M. Ekici, M. Mirzazadeh, Q. Zhou, A. S. Alshomrani, S. P. Moshokoa and M Belic, Optical soliton perturbation with fractional temporal evolution by extended G0/G expansion method, Optik 161 (2018), 301 – 320, DOI: 10.1016/j.ijleo.2018.02.051.
A. Ebaid and E. H. Aly, Exact solutions for the transformed reduced Ostrovsky equation via the F-expansion method in terms of Weierstrass-elliptic and Jacobian-elliptic functions, Wave Motion 49 (2012), 296 – 308, DOI: 10.1016/j.wavemoti.2011.11.003.
A. Ebaid, An improvement on the Exp-function method when balancing the highest order linear and nonlinear terms, Journal of Mathematical Analysis and Applications 392 (2012), 1 – 5, DOI: 10.1016/j.jmaa.2011.04.025.
M. Ekici, M. Mirzazadeh, A. Sonmezoglu, Q. Zhou, H. Triki, M. Z. Ullah, S. P. Moshokoa and A. Biswas, Optical solitons in birefringent fibers with Kerr nonlinearity by exp-function method, Optik 131 (2017), 964 – 976, DOI: 10.1016/j.ijleo.2016.12.015.
A. A. El-Satar, Similarity reductions and new exact solutions for B-family equations, American Journal of Mathematics and Statistics 2(3) (2012), 40 – 43, DOI: 10.5923/j.ajms.20120203.05.
A. A. Gaber, A. F. Aljohani, A. Ebaid and J. T. Machado, The generalized version of Kudryashov method for nonlinear space-time fractional partial differential equations of Burgers type, Nonlinear Dynamics 95 (2019), 361 – 368, DOI: 10.1007/s11071-018-4568-4.
A. A. Gaber and M. H. Shehata, New approach of MHD boundary layer flow towards a porous stretching sheet via symmetry analysis and the generalized Exp-function method, International Journal of Analysis and Applications 18(5) (2020), 738 – 747, DOI: 10.28924/2291-8639-18-2020-738.
J.-H. He and M. A. Abdou, New periodic solutions for non-linear evolution equations using Exp-function method, Chaos, Solitons & Fractals 34 (2007), 1421 – 1429, DOI: 10.1016/j.chaos.2006.05.072.
K. Hosseini, A. Bekir and R. Ansari, New exact solutions of the conformable time-fractional Cahn-Allen and Cahn-Hilliard equations using the modified Kudryashov method, Optik 132 (2017), 203 – 209, DOI: 10.1016/j.ijleo.2016.12.032.
A.-A. Hyder and M. A. Barakat, General improved Kudryashov method for exact solutions of nonlinear evolution equations in mathematical physics, Physica Scripta 4(95) (2020), 045212, DOI: 10.1088/1402-4896/ab6526.
M. M. Kabir, A. Khajeh, E. A. Aghdam and A. Y. Koma, Modified Kudryashov method for finding exact solitary wave solutions of higher-order nonlinear equations, Mathematical Methods in the Applied Sciences 34 (2011), 213 – 219, DOI: 10.1002/mma.1349.
M. M. A. Khater, A. R. Seadawy and D. Lu, Dispersive optical soliton solutions for higher order nonlinear Sasa-Satsuma equation in mono mode fibers via new auxiliary equation method, Superlattices and Microstructures 113 (2018), 346 – 358, DOI: 10.1016/j.spmi.2017.11.011.
D. Kumar, A. R. Seadawy and A. K. Joardar, Modified Kudryashov method via new exact solutions for some conformable fractional differential equations arising in mathematical biology, Chinese Journal of Physics 56 (2018), 75 – 85, DOI: 10.1016/j.cjph.2017.11.020.
J.-G. Liu, L. Zhou and Y. He, Multiple soliton solutions for the new (2í…1)-dimensional Korteweg-de Vries equation by multiple exp-function method, Applied Mathematics Letters 80 (2018), 71 – 78, DOI: 10.1016/j.aml.2018.01.010.
Z. Y. Ma, Homotopy perturbation method for the Wu-Zhang equation in fluid dynamics, Journal of Physics: Conference Series 96 (2008), 012182, DOI: 10.1088/1742-6596/96/1/012182.
J. Manafian, M. F. Aghdaei, M. Khalilian and R. S. Jeddi, Application of the generalized G0/G expansion method for nonlinear PDEs to obtaining soliton wave solution, Optik 135 (2017), 395 – 406, DOI: 10.1016/j.ijleo.2017.01.078.
M. H. M. Moussa and A. A. Gaber, Symmetry analysis and solitary wave solutions of nonlinear ion-acoustic waves equation, International Journal of Analysis and Applications 18 (2020), 448 – 460, DOI: 10.28924/2291-8639-18-2020-448.
I. Naeem and M. D. Khan, Symmetry classification of time-fractional diffusion equation, Communications in Nonlinear Science and Numerical Simulation 42 (2017), 560 – 570, DOI: 10.1016/j.cnsns.2016.05.022.
Rahmatullah, R. Ellahi, S. T. Mohyud-Din and U. Khan, Exact traveling wave solutions of fractional order Boussinesq-like equations by applying Exp-function method, Results in Physics 8 (2018), 114 – 120, DOI: 10.1016/j.rinp.2017.11.023.
S. Sahoo and S. S. Ray, Invariant analysis with conservation laws for the time fractional Drinfeld-Sokolov-Satsuma-Hirota equations, Chaos, Solitons and Fractals 104 (2017), 725 – 733, DOI: 10.1016/j.chaos.2017.09.031.
A. M. Shahoot, K. A. E. Alurrfi, M. O. M. Elmrid, A. M. Almsiri and A. M. H. Arwiniya, The G0/G expansion method for solving a nonlinear PDE describing the nonlinear low-pass electrical lines, Journal of Taibah University for Science 13 (2018), 63 – 70, DOI: 10.1080/16583655.2018.1528663.
N. Xiong, Y.-Q. Li, J. O. Chen and Y. Chen, One-dimensional optimal system and similarity reductions of Wu-Zhang equation, Communications in Theoretical Physics 66 (2016), 1 – 11, URL: https://ctp.itp.ac.cn/EN/Y2016/V66/I01/1.
P. Ye and G. Cai, An extended (G0/G)-expansion method and travelling wave solutions to nonlinear Klein-Gordon equation, International Journal of Nonlinear Science 11 (2011), 225 – 229, URL: http://www.internonlinearscience.org/upload/papers/20110915021935124.pdf.
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