| Citation: |
Asim Zafar, Ahmet Bekir. EXPLORING THE CONFORMABLE TIME-FRACTIONAL (3 + 1)-DIMENSIONAL MODIFIED KORTEWEG-DEVRIESZAKHAROV- KUZNETSOV EQUATION VIA THREE INTEGRATION SCHEMES[J]. Journal of Applied Analysis & Computation, 2021, 11(1): 161-175. doi: 10.11948/20190205
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EXPLORING THE CONFORMABLE TIME-FRACTIONAL (3 + 1)-DIMENSIONAL MODIFIED KORTEWEG-DEVRIESZAKHAROV- KUZNETSOV EQUATION VIA THREE INTEGRATION SCHEMES
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Abstract
In this paper, the nonlinear conformable time-fractional (3 + 1)- dimensional modified KdV-Zakharov-Kuznetsov equation is being explored using three well-established integration schemes named as: the expζ function method, the hyperbolic function and modified Kudryashov schemes. In returns, many new exact solitary wave solutions, including rational, dark, singular and combined dark-singular solitons, are obtained and have been compared with those given in the literature. Moreover, the obtained solutions are demonstrated by 2D and 3D graphs for suitable values of the parameters to observe the dynamical behavior of the secured solutions. -
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References
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Asim Zafar, Ahmet Bekir. EXPLORING THE CONFORMABLE TIME-FRACTIONAL (3 + 1)-DIMENSIONAL MODIFIED KORTEWEG-DEVRIESZAKHAROV- KUZNETSOV EQUATION VIA THREE INTEGRATION SCHEMES[J]. Journal of Applied Analysis & Computation, 2021, 11(1): 161-175. doi: 10.11948/20190205
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Figure 1.
$ 2D $ and 3D plots for the solutions$ V_{1} $ appear in Eq.k__ge (15) taking$ y=1 $ and$ z=0 $ -
Figure 2. 2D and 3D plots for the solutions
$ V_{1} $ appear in Eq.k__ge (15) taking$ y=1 $ and$ z=0 $ -
Figure 3. 2D and 3D plots for the solutions
$ V_{2} $ appear in Eq.k__ge (16) taking$ y=1 $ and$ z=0 $ -
Figure 4. 2D and 3D plots for the solutions
$ V_{2} $ appear in Eq.k__ge (16) taking$ y=1 $ and$ z=0 $ -
Figure 5. 2D and 3D plots for the solutions
$ u_{1, 2} $ appear in Eq.k__ge (18) taking$ y=1 $ and$ z=0 $ -
Figure 6. 2D and 3D plots for the solutions
$ u_{1, 2} $ appear in Eq.k__ge (18) corresponding to$ y=1 $ ,$ z=0 $ -
Figure 7. 2D and 3D plots for the solutions
$ u_{3, 4} $ appear in Eq.k__ge (19) taking$ y=1 $ and$ z=0 $ -
Figure 8. 2D and 3D plots for the solutions
$ u_{3, 4} $ appear in Eq.k__ge 19 taking$ y=1 $ and$ z=0 $ -
Figure 9. 2D and 3D plots for the solutions
$ V_{9, 10} $ appear in Eq.k__ge (22) corresponding to$ y=1 $ ,$ z=0 $ -
Figure 10. 2D and 3D plots for the solutions
$ V_{9, 10} $ appear in Eq.k__ge (22) corresponding to$ y=1 $ ,$ z=0 $ -
Figure 11. 2D and 3D plots for the solutions
$ V_{1, 2} $ appear in Eq.(28) corresponding to$ y=1 $ and$ z=0 $ -
Figure 12. 2D and 3D plots for the solutions
$ V_{1, 2} $ appear in Eq.k__ge (28) corresponding to$ y=1 $ and$ z=0 $