| Citation: |
Jingyu Xu, Zongguo Zhang, Huanhe Dong, Hongwei Yang. BÄCKLUND TRANSFORMATIONS AND ROUGE WAVES IN THE FRAME OF A FRACTIONAL ORDER MODEL IN MAGNETIZED DUSTY PLASMA[J]. Journal of Applied Analysis & Computation, 2022, 12(5): 1842-1860. doi: 10.11948/20210379
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BÄCKLUND TRANSFORMATIONS AND ROUGE WAVES IN THE FRAME OF A FRACTIONAL ORDER MODEL IN MAGNETIZED DUSTY PLASMA
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Abstract
Dusty plasma has become a hot topic in physics in recent years because of its wide application in the space environment, industrial processing and fusion reaction. The (3+1)-dimensional modified Zakharov-Kuznetsov (mZK) equation describing waves propagation in dusty plasma is derived via the reduced perturbation method, based on the governing equation. Furthermore, integer-order equation is derived as the fractional modified Zakharov-Kuznetsov (TF-mZK) equation. The exact solution and B$ \ddot{a} $cklund transformation are obtained by the fractional transformation and Bell polynomials. Finally, the rouge wave phenomenon in magnetized dusty plasma is described, and the effects of fractional order, phase velocity and dust-cyclotron frequency on the propagation characteristics of dust acoustic rogue waves are analyzed.
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References
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Jingyu Xu, Zongguo Zhang, Huanhe Dong, Hongwei Yang. BÄCKLUND TRANSFORMATIONS AND ROUGE WAVES IN THE FRAME OF A FRACTIONAL ORDER MODEL IN MAGNETIZED DUSTY PLASMA[J]. Journal of Applied Analysis & Computation, 2022, 12(5): 1842-1860. doi: 10.11948/20210379
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Figure 1. The profile of Eq. (4.17) with
$ p=1.6, k_{1}=1.99, q=0.1, \lambda=0.8, \Omega=0.6, d_{1}=0.5, d_{3}=1, \omega=1, \zeta=0, \eta=1. $ -
Figure 2. The profile of Eq. (4.17) with
$ k_{1}=1.99, p=1.6, d_{1}=0.5, d_{3}=1, \omega=1, \tau=\zeta =0. $ -
Figure 3. The profile of Eq. (4.17) with
$ k_{1}=1.2, p=1.65, q=0.1, d_{1}=1.5, d_{3}=2.57, \omega=1, \tau=\eta =0. $ -
Figure 4. The panels show the evolution of the dust acoustic rogue waves. The parameters are
$ k_{1}=1.99, p=1.6, q=0.1, \lambda=0.8, \Omega=0.6, d_{1}=0.5, d_{3}=1, \eta=1 $ and$ \zeta=0. $ -
Figure 5. The panels show the evolution of the dust acoustic rogue waves.The parameters are
$ k_{1}=1.99, p=1.6, q=0.1, \lambda=0.8, \Omega=0.6, d_{1}=0.5, d_{3}=1, \eta=1 $ and$ \zeta=0. $ -
Figure 6. The profile of Eq. (4.17) by choosing
$ k_{1}=1.9, p=1.5, q=0.5, d_{1}=1, d_{3}=1, \zeta=0. \omega=1, \xi=9, \tau=\eta=1, $