Analysis of Entropy-dependent solitons in ETG-driven magneto plasma by Variational Iteration Method


  • Tasawar Abbas Department of Mathematics, University of Wah, Wah Cantt, 47040
  • Ehsan Ul Haq Department of Mathematics, Hong Kong Baptist University, Kowloon Tong Kowloon, Hong Kong.
  • Ambreen Ayub Department of Physics, Women University Swabi. Swabi Khyber Pakhtunkhwa
  • Asadullah Dawood Department of Physics, National Excellence Institute (University), Islamabad; 04524



Nowadays, the discovery of the link between entropy and plasma density and temperature opens up new avenues for mathematicians and researchers to examine alternative plasma models in terms of entropy. The linear dispersion relation and KdV equation are created after the entropy drift is taken into account in the ETG mode. In addition, the Variational Iteration Technique (VIM) is used to determine the problem’s analytical solutions. Involving the Langrange multiplier also helps to accelerate computation and lower its cost. Then, it is shown that in ETG mode, entropy impacts both the breadth and amplitude of rarefactive solitons, as well as the impact of inhomogeneity drift and the magnetic field on the configuration of solitons. In this instance, however, only the rarefactive solitons are present. Since introducing entropy to the system might alter the previous plasma findings, this study is new. Finally, the current approach will be applied to the entropy-based in magnetically restrained plasmas, solitary waves can be observed. The graphical findings are also provided using Maple-18.


Azimi, L., Mirza, A. M. and Khan, M. Y. [2006], ‘Nonlinear dynamics of electrostatic ion-temperaturegradient modes in a dust-contaminated plasma with variable charge and sheared ion flows’, Physics of Plasmas 13, 082302.

Bell, A. R., Kingham, R. J., Watkins, H. C. and Matthews, J. H. [2020], ‘Instability in a magnetised collisional plasma driven by a heat flow or a current’, Plasma Physics and Controlled Fusion 62(9), 095026.

Bharuthram, R. and Shukla, P. K. [1987], ‘Electron pressure gradient-driven short-wavelength driftwave instability and its nonlinear evolution’, Plasma Physics and Controlled Fusion 29(12), 1695.

Boström, R., Gustafsson, G., Holback, B., Holmgren, G., Koskinen, H. and Kintner, P. [1988], ‘Characteristics of solitary waves and weak double layers in the magnetospheric plasma’, Phys. Rev. Lett. 61(7), 82–85.

Brantov, A. V., Bychenkov, V. Y. and Rozmus, W. [2012], ‘Electrostatic response of a two-component plasma with coulomb collisions’, Phys. Rev. Lett. 108(20), 205001.

Brissaud, J. [2005], ‘The meanings of entropy’, Entropy 7, 68–96.

Correa, R. A. C., da Rocha, R. and de Souza Dutra, A. [n.d.a], ‘Information-entropic for travelling solitons in lorentz and cpt breaking systems’, High Energy Physics - Theory .

Correa, R., da Rocha, R. and de Souza Dutra, A. [n.d.b], ‘Entropic information for travelling solitons in lorentz and CPT breaking systems’, Annals of Physics .

Dewar, R. L., Hole, M. J., McGann, M., Mills, R. and Hudson, S. R. [2008], ‘Relaxed plasma equilibria and entropy-related plasma self organization principles’, Entropy 10(4), 621–634.

Dewar, R., Yoshida, Z., Bhattacharjee, A. and Hudson, S. [2015], ‘Relaxed plasma equilibria and entropy-related plasma self organization principles’, Journal of Plasma Physics 81(6), 621–634.

Dvali, G. [2021a], ‘Entropy bound and unitarity of scattering amplitudes’, Journal of High Energy Physics 2021(3).

Dvali, G. [2021b], ‘Unitarity entropy bound of solitons and instantons’, Fortsch. Phys 69(1), 2000091.

Dyachenko, A. I., Nazarenko, S. V. and Zakharov, V. E. [1992], ‘Wave-vortex dynamics in drift and βplane turbulence’, Physics Letters A 165(4), 330–334.

Garbet, X., Dubuit, N., Asp, E., Sarazin, Y., Bourdelle, C., Ghendrih, P. and Hoang, G. T. [2005], ‘Turbulent fluxes and entropy production rate’, Physics of Plasmas 12(8), 082511.

Ghosh, U. N., Nasipuri, S. and Chatterjee, P. [2022], ‘Study of lump soliton structures in quantum electron-positron-ion magnetoplasma’, Contributions to Plasma Physics 62, e202200094.

Goswami, J., Chandra, S. and Ghosh, B. [2019], ‘Shock waves and the formation of solitary structures in electron acoustic wave in inner magnetosphere plasma with relativistically degenerate particles’, Astrophysics and Space Science 364(4).

Haq, E. U., Khan, S. U., Abbas, T., Smida, K., Hassan, Q. M. U., Ahmad, B., Khan, M. I., Guedri, K., Kumam, P. and Galal, A. M. [2022], ‘Numerical aspects of thermo migrated radiative nanofluid flow towards a moving wedge with combined magnetic force and porous medium’, Scientific reports 12(1), 10120.

Haq, E.U.; Abbas, T. H. Q. A. B. [2021], ‘Analysis of recent analytical techniques on the kdvb equation’, J. Sci. Technol. Arts 21, 1143–1152.

Haque, Q. [2012], ‘Electrostatic drift shocks and drift wave instability in inhomogeneous rotating electron-positron-ion plasmas’, Physics of Plasmas 19(9), 092102.

He, J.-H. [1999], ‘Variational iteration method – a kind of non linear analytical technique’, International Journal of Non-Linear Mechanics 34(4), 699–708.

Iqbal, J. and Khan, M. Y. [2017], ‘Soliton formation in ion temperature gradient driven magnetoplasma’, Physics of Plasmas 24(4), 042506.

Khan, A., Zakir, U., Haque, Q. U. and Qamar, A. [n.d.], ‘Role of entropy in i-mode driven nonlinear structures obtained by homotopy perturbation method in electron-positron-ion plasma’, Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences 76(8).

Khan, M. Y. and Iqbal, J. [2017], ‘Effect of entropy on soliton profile in itg driven magneto-plasma’, Physics of Plasmas 24(8).

Kobayashi, S., Gürcan, D. and Diamond, P. H. [2015], ‘Direct identification of predator-prey dynamics in gyrokinetic simulations’, Physics of Plasmas 22(9), 090702.

Kobayashi, S., Rogers, B. N. and Dorland, W. [2010], ‘Particle pinch in gyrokinetic simulations of closed field-line systems’, Phys. Rev. Lett. 105(23), 235004.

Liu, C. S. [1971], ‘Instabilities in a magnetoplasma with skin current’, Physical Review Letters 27(12), 1637–1640.

Müller, M., Schmalian, J. and Fritz, L. [2009], ‘Graphene a nearly perfect fluid’, Phys. Rev. Lett. 103(2), 025301.

Nielsen, A. H., Rasmussen, J. and Schmidt, M. R. [n.d.], ‘Self organization and coherent structures in plasmas and fluids’, Physica Scripta 63, 49–58.

Pegoraro, F., Bonfiglio, D., Cappello, S., Giannatale, G. D., Falessi, M. V., Grasso, D. and Veranda, M. [2019], ‘Coherent magnetic structures in self-organized plasmas’, Plasma Physics and Controlled Fusion 61(4), 044003.

Razumova, K. A., Andreev, V. F., Kasyanova, N. V. and Lysenko, S. E. [2020], ‘Explanation of experimentally observed phenomena in hot tokamak plasmas from the nonequilibrium thermodynamics position’, Entropy 22(1).

Rehan, M., Zakir, U., Haque, Q. and Hameed, G. [2020], ‘Ion temperature gradient mode driven solitons and shocks in superthermal plasma’, Chinese Journal of Physics 68, 908–918.

Sabry, R., Moslem, W. M., Haas, F., Ali, S. and Shukla, P. K. [2008], ‘Nonlinear structures: Explosive, soliton, and shock in a quantum electron-positron-ion magnetoplasma’, Physics of Plasmas 15(12), 122308.

Tasso, H. [1967], ‘Shock-like drift waves’, Physics Letters A 24(11), 618.

Yaqub Khan, M., Iqbal, J. and ul Haq, A. [2014], ‘Effect of entropy on anomalous transport in electrontemperature-gradient-modes’,

Physics of Plasmas 21(5), 052308.

Yaqub Khan, Qaiser Manzoor, M., Haq, A. u. and Iqbal, J. [2017], ‘Effect of entropy on anomalous transport in ITG-modes of magneto-plasma’, Nuclear Fusion 57(4), 046027.

Yasmin, H. and Iqbal, N. [2022], ‘A comparative study of the fractional coupled burgers and hirotandash;satsuma kdv equations via analytical techniques’, Symmetry 14(7).

Zakir, U., Adnan, M., Haque, Q., Qamar, A. and Mirza, A. M. [2016a], ‘Ion temperature gradient mode driven solitons and shocks’, Physics of Plasmas 23(4).

Zakir, U., Adnan, M., Haque, Q., Qamar, A. and Mirza, A. M. [2016b], ‘Ion temperature gradient mode driven solitons and shocks’, Physics of Plasmas 23(4), 042104.

Zhang, Y. Q., DeSilva, A. W. and Mostovych, A. N. [1989], ‘Density fluctuation spectra of a collisiondominated plasma measured by light scattering’, Phys. Rev. Lett. 62(16), 1848–1851.




How to Cite

Abbas, T., Haq, E. U., Ayub, A., & Dawood, A. (2022). Analysis of Entropy-dependent solitons in ETG-driven magneto plasma by Variational Iteration Method. VFAST Transactions on Mathematics, 10(2), 34–51.