Article
Solitons and other solutions of (3 + 1)-dimensional space–time fractional modified KdV–Zakharov–Kuznetsov equation
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Abstract
In the current paper, we carry out an investigation into the exact solutions of the (3+1)-dimensional space-time fractional modified KdV–Zakharov–Kuznetsov (fractional mKdV–ZK) equation. Based on the conformable fractional derivative and its properties, the fractional mKdV–ZK equation is reduced into an ordinary differential equation which has been solved analytically by the variable separated ODE method. Various types of analytic solutions in terms of hyperbolic functions, trigonometric functions and Jacobi elliptic functions are derived. All conditions for the validity of all obtained solutions are given.
Keywords
The (3+1)-dimensional space-time fractional mKdV–ZK, the variable separated ODE method, solitons and periodic wave solutions, 35A24, 35C08, 35Q53
Citation
Al-Ghafri, K. S. & Rezazadeh, H. (2019). Solitons and other solutions of (3 + 1)-dimensional space–time fractional modified kdv–zakharov–kuznetsov equation. Applied Mathematics and Nonlinear Sciences, 4(2), 289–304. https://doi.org/10.2478/AMNS.2019.2.00026
K. S. Al-Ghafri and H. Rezazadeh, “Solitons and other solutions of (3 + 1)-dimensional space–time fractional modified kdv–zakharov–kuznetsov equation,” Applied Mathematics and Nonlinear Sciences, vol. 4, no. 2, pp. 289–304, 2019, doi: 10.2478/AMNS.2019.2.00026.
Al-Ghafri KS, Rezazadeh H. Solitons and other solutions of (3 + 1)-dimensional space–time fractional modified kdv–zakharov–kuznetsov equation. Applied Mathematics and Nonlinear Sciences. 2019;4(2):289–304. doi:10.2478/AMNS.2019.2.00026.
Al-Ghafri, K. S. and Rezazadeh, H. (2019), ‘Solitons and other solutions of (3 + 1)-dimensional space–time fractional modified kdv–zakharov–kuznetsov equation’, Applied Mathematics and Nonlinear Sciences, 4(2), pp. 289–304. Available at: https://doi.org/10.2478/AMNS.2019.2.00026.
Al-Ghafri, K. S., and Hadi Rezazadeh. “Solitons and Other Solutions of (3 + 1)-dimensional Space–time Fractional Modified Kdv–zakharov–kuznetsov Equation.” Applied Mathematics and Nonlinear Sciences, vol. 4, no. 2, 2019, pp. 289–304. https://doi.org/10.2478/AMNS.2019.2.00026.
Al-Ghafri, K. S., and Hadi Rezazadeh. “Solitons and Other Solutions of (3 + 1)-dimensional Space–time Fractional Modified Kdv–zakharov–kuznetsov Equation.” Applied Mathematics and Nonlinear Sciences 4, no. 2 (2019): 289–304. https://doi.org/10.2478/AMNS.2019.2.00026.
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Published by: Engineering Journals
