Existence of Small Amplitude KDV and MKDV Solitons in a Magnetized Dusty Plasma with q−Nonextensive Distributed Electrons
Abstract
The existence and propagating characteristics of small amplitude dust-ion-acoustic (DIA) Korteweg-de Vries (KdV) and modified KdV solitons in a three component magnetized plasma composed of positive inertial ions with pressure variation, noninertial electrons and negative charged immobile dust grains are theoretically and numerically investigated when the electrons obey a q-nonextensive velocity distribution. Utilizing the reductive perturbation method, to derive KdV and modified KdV equations and obtain the DIA soliton solutions along with the corresponding small amplitude potentials. This study shows that there are compressive and/or rarefactive solitons and no soliton at all, due to the parametric dependency on the first-order nonlinear coefficient through the number density of positive ions and negative dust grains and the electron nonextensivity. The coexistence of compressive and rarefactive solitons appears by raising the measure of nonlinearity coefficient to the second-order using the modified KdV equation. The properties such as speed, amplitude, width etc. of the propagating soliton are numerically discussed.
Downloads
References
C. Thompson, A. Barkan, N. D’angelo, and R. L. Merlino, ”Dust acoustic waves in a direct current glow discharge,” Phys. Plasmas, 4(7), 2231-2353 (1997). https://doi.org/10.1063/1.872238
N.N. Rao, P.K. Shukla, and M.Y. Yu, ”Dust-acoustic waves in dusty plasmas.” Planet. Space Sci. 38(4), 543–546 (1990). https://doi.org/10.1016/0032-0633(90)90147-I
P.K. Shukla, and V.P. Silin, ”Dust ion-acoustic wave”. Phys. Scr. 45(5), 508 (1992). https://dx.doi.org/10.1088/0031-8949/45/5/015
P.V. Bliokh, and V.V. Yaroshenko, ”Electrostatic waves in saturns rings,” Soviet Astron. 29, 330–336 (1985). https://adsabs.harvard.edu/full/1985SvA....29..330B
M. Rosenberg, ”On dust wave instabilities in collisional magnetized plasmas,” IEEE Trans. Plasma Sci. 44(4), 451–457 (2016). https://doi.org/10.1109/TPS.2015.2499119
P.K. Shukla, M.Y. Yu, and R. Bharuthram, ”Linear and nonlinear dust drift waves,” J. Geophys. Res.: Space Sci. 96(A12), 21343–21346 (1991). https://doi.org/10.1029/91JA02331
F. Melandso, ”Lattice waves in dust plasma crystals,” Phys. Plasmas, 3(11), 3890–3901 (1996). https://doi.org/10.1063/1.871577
R.L. Merlino, A. Barkan, C. Thompson, and N. D’Angelo, ”Laboratory studies of waves and instabilities in dusty plasmas,” Phys. Plasmas, 5(5), 1607–1614 (1998). https://doi.org/10.1063/1.872828
S. Ghosh, S. Sarkar, M. Khan, and M.R. Gupta, ”Nonlinear properties of small amplitude dust ion acoustic solitary waves,” Phys. Plasmas, 7(9), 3594–3599 (2000). https://doi.org/10.1063/1.1287140
B.C. Kalita, S. Das, and D. Bhattacharjee, ”Determination of the measure of size (amplitude) of perturbation and its role in the process of enforcing discrete Korteweg-de Vries solitons to modified Korteweg-de Vries solitons as means of continuum hypothesis in a multi-component dusty plasma,” Phys. Plasmas, 24(10), 102121 (2017). https://doi.org/10.1063/1.5005535
S. Das and D.C. Das, ”Compressive and rarefactive dust ion-acoustic korteweg–de vries and modified korteweg–devries solitons in a multi-component dusty plasma,” J. Korean Phys. Soc. 83, 328 (2023). https://doi.org/10.1007/s40042-023-00892-w
R. Khanam, M. Rahman, and S.N. Barman, ”Nonlinear propagation of ion acoustic solitary waves in weakly relativistic plasmas with positive and negative ions: The effect of electron inertia,” Adv. Appl. Fluid Mech. 30(2), 169–185 (2023). https://doi.org/10.17654/0973468623010
Y. Nakamura, and A. Sarma, ”Observation of ion-acoustic solitary waves in a dusty plasma,” Phys. Plasmas, 8(9), 3921–3926 (2001). https://doi.org/10.1063/1.1387472
X. Liang, J. Zheng, J.X. Ma, W.D. Liu, J. Xie, G. Zhuang, and C.X. Yu, ”Experimental observation of ion-acoustic waves in an inhomogeneous dusty plasma,” Phys. Plasmas, 8(5), 1459–1462 ()2001). https://doi.org/10.1063/1.1362530
S. Ghosh, S. Sarkar, M. Khan, and M.R. Gupta, ”Small amplitude nonlinear dust ion acoustic waves in a magnetized dusty plasma with charge fluctuation,” Phys. Scr. 63(5), 395 (2001), https://dx.doi.org/10.1238/Physica.Regular.063a00395
M.G.M. Anowar, and A.A. Mamun, ”Dust ion-acoustic solitary waves in a hot adiabatic magnetized dusty plasma,” Phys. Lett. A, 372(37), 5896–5900 (2008). https://doi.org/10.1016/j.physleta.2008.07.056
T. Saha, and P. Chatterjee, ”Obliquely propagating ion acoustic solitary waves in magnetized dusty plasma in the presence of nonthermal electrons,” Phys. Plasmas, 16(1), 013707 (2009). https://doi.org/10.1063/1.3067824
M. Shahmansouri, and H. Alinejad, ”Arbitrary amplitude dust ion acoustic solitary waves in a magnetized suprathermal dusty plasma,” Phys. Plasmas, 19(12), 123701 (2012). https://doi.org/10.1063/1.4769850
A.P. Misra, and A. Barman, ”Oblique propagation of dust ion-acoustic solitary waves in a magnetized dusty pair-ion plasma,” Phys. Plasmas, 21(7), 073702 (2014). https://doi.org/10.1063/1.4886125
A. Atteya, S. Sultana, and R. Schlickeiser, ”Dust-ion-acoustic solitary waves in magnetized plasmas with positive and negative ions: The role of electrons superthermality,” Chinese J. Phys. 56(5), 1931–1939 (2018). https://doi.org/10.1016/j.cjph.2018.09.002
N. Zerglaine, K. Aoutou, and T.H. Zerguini, ”Propagation of dust ion acoustic wave in a uniform weak magnetic field,” Astrophys. Space Sci. 364, 84 (2019). https://doi.org/10.1007/s10509-019-3573-5
Md.R. Hassan, and S. Sultana, ”Damped dust-ion-acoustic solitons in collisional magnetized nonthermal plasmas,” Contr. Plasma Phys. 61(9), e202100065 (2021). https://doi.org/10.1002/ctpp.202100065
S.Md. Abdus, A.Md. Ali, and A.Md. Zulfikar, ”Higher-order nonlinear and dispersive effects on dust-ion-acoustic solitary waves in magnetized dusty plasmas,” Results Phys. 32, 105114, (2022). https://doi.org/10.1016/j.rinp.2021.105114
A. R´enyi, ”On a new axiomatic theory of probability,” Acta Mathematica Academiae Scientiarum Hungaricae, 6(3-4), 285–335 (1955). https://doi.org/10.1007/BF02024393
C. Tsallis, ”Possible generalization of boltzmann-gibbs statistics,” J. Stat. Phys. 52, 479–487 (1988). https://doi.org/10.1007/BF01016429
M. Tribeche, L. Djebarni, and R. Amour, ”Ion-acoustic solitary waves in a plasma with a q-nonextensive electron velocity distribution,” Phys. Plasmas, 17(4), 042114 (2010). https://doi.org/10.1063/1.3374429
H.R. Pakzad, ”Effect of q-nonextensive electrons on electron acoustic solitons,” Phys. Scr. 83(1), 015505 (2010). https://dx.doi.org/10.1088/0031-8949/83/01/015505
U.K. Samanta, A. Saha, and P. Chatterjee, ”Bifurcations of dust ion acoustic travelling waves in a magnetized dusty plasma with a q-nonextensive electron velocity distribution,” Phys. Plasmas, 20(2), 022111 (2013). https://doi.org/10.1063/1.4791660
A.A. Mahmoud, E.M. Abulwafa, A.F. Al-Araby, and A.M. Elhanbaly, ”Plasma parameters effects on dust acoustic solitary waves in dusty plasmas of four components,” Adv. Math. Phys. 11, 7935317 (2018). https://doi.org/10.1155/2018/7935317
F. Araghi, S. Miraboutalebi, and D. Dorranian, ”Effect of variable dust size, charge and mass on dust acoustic solitary waves in nonextensive magnetized plasma,” Indian J. Phys. 94, 547–554 (2020). https://doi.org/10.1007/s12648-019-01488-6
P. Eslami, M. Mottaghizadeh, and H.R. Pakzad, ”Nonplanar dust acoustic solitary waves in dusty plasmas with ions and electrons following a q-nonextensive distribution,” Phys. Plasmas, 18(10), 102303 (2011). https://doi.org/10.1063/1.3642639
A. Saha, and P. Chatterjee, ”Propagation and interaction of dust acoustic multi-soliton in dusty plasmas with q-nonextensive electrons and ions,” Astrophys. Space Sci. 353, 169–177 (2014). https://doi.org/10.1007/s10509-014-2028-2
P. Chatterjee, K. Roy, and U.N. Ghosh, Waves and Wave Interactions in Plasmas, (World Scientific Publishing Co. Pte. Ltd., 2022), pp. 25-28.
M. Tribeche, L. Djebarni, and R. Amour, ”Ion-acoustic solitary waves in a plasma with a q-nonextensive electron velocity distribution,” Phys. Plasmas, 17(4), 042114 (2010). https://doi.org/10.1063/1.3374429
U.N. Ghosh, P. Chatterjee, and S.K. Kundu, ”The effect of q-distributed ions during the head-on collision of dust acoustic solitary waves,” Astrophys. Space Sci. 339, 255–260 (2012). https://doi.org/10.1007/s10509-012-1009-6
G. Ullah, M. Saleem, M. Khan, M. Khalid, A. Rahman, and S. Nabi, ”Ion acoustic solitary waves in magnetized electron–positron–ion plasmas with tsallis distributed electrons,” Contr. Plasma Phys. 60(10), e202000068 (2020). https://doi.org/10.1002/ctpp.202000068
J. Tamang, A. Abdikian, and A. Saha, ”Phase plane analysis of small amplitude electronacoustic supernonlinear and nonlinear waves in magnetized plasmas,” Phys. Scr. 95(10), 105604 (2020). https://dx.doi.org/10.1088/1402-4896/abb05b
F. Verheest, ”Oblique propagation of solitary electrostatic waves in multispecies plasmas,” J. Phys. A: Math. Theor. 42(28), 285501 (2009). https://dx.doi.org/10.1088/1751-8113/42/28/285501
Copyright (c) 2024 Muktarul Rahman, Satyendra Nath Barman
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
