Numerical Analysis of Nonlinear Electron Acoustic Lump Solitons in a Homogeneous, Unmagnetized, Collision less Plasma

K. H. Shah; Asad Ali; Ahmar Manzoor; Muhammad Imran; Muhammad Hanif

Authors

K. H. Shah Department of Physics, University of Narowal, 51600 Narowal, Pakistan
Asad Ali Department of Physics, University of Narowal, 51600 Narowal, Pakistan
Ahmar Manzoor Department of Physics, Government College University, Lahore 54000, Pakistan
Muhammad Imran Department of Electronics, Institute of Physics, Government College University, Lahore 54000, Pakistan
Muhammad Hanif Department of Mathematics, University of Narowal, 51600 Narowal, Pakistan

Keywords:

Electron Acoustic Waves, ΚP Equation, Kappa Distribution, Lump Solitons, Numerical Analysis

Abstract

Electron-acoustic waves in a homogeneous, unmagnetized, collisionless plasma composed ofinertial cold electrons, κ-distributed hot electrons, and stationary ions are investigated. Starting from the fluid equations coupled with Poisson’s equation, the reductive perturbation method is systematically applied with appropriate stretched coordinates to derive a two-dimensional Kadomtsev–Petviashvili (KP) equation governing the weakly nonlinear evolution of electron-acoustic perturbations, including weak transverse effects. The nonlinear and dispersive coefficients of the KP equation are obtained explicitly in terms of the plasma density ratio and the superthermality index κ. Exact lump soliton solutions are then constructed using a rational-function approach, yielding fully localized two-dimensional structures that decay algebraically in space. Parametric analysis shows that κ significantly influences the amplitude and localization of the lump solitons; lower κ values enhance nonlinearity and produce higher, more localized structures, whereas larger κ leads to broader and weaker excitations. These results clarify the role of super thermal electrons in multidimensional nonlinear wave dynamics.

References

R. E. E. R. Pottelette, “Modulated electron-acoustic waves in auroral density cavities: FAST observations,” Geophys. Res. Lett., vol. 26, no. 16, pp. 2629–2632, 1999, [Online]. Available: https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1999GL900462

H. Matsumoto, X. H. Deng, H. Kojima, R. R. Anderson, “Observation of Electrostatic Solitary Waves associated with reconnection on the dayside magnetopause boundary,” Geophys. Res. Lett., 2003, [Online]. Available: https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2002GL016319

C. W. C. R. E. Ergun, “FAST satellite observations of large-amplitude solitary structures,” Geophys. Res. Lett., vol. 25, no. 12, pp. 2041–2044, 1998, [Online]. Available: https://experts.umn.edu/en/publications/fast-satellite-observations-of-large-amplitude-solitary-structure/

M. Berthomier, R. Pottelette, M. Malingre, and Y. Khotyaintsev, “Electron-acoustic solitons in an electron-beam plasma system,” Phys. Plasmas, vol. 7, no. 7, pp. 2987–2994, 2000, doi: 10.1063/1.874150.

Yuequn Lou, Binbin Ni, Xing Cao, Qianli Ma, Yoshizumi Miyoshi, Dedong Wang, Shuqin Chen, “Distinct Global Distribution of Electrostatic Electron Cyclotron Harmonic Waves in Earth’s Magnetosphere Revealed by Multi-Satellite Observations,” Geophys. Res. Lett., 2025, doi: https://doi.org/10.1029/2025GL117276.

S. P. Gary, “Theory of space plasma microinstabilities,” p. 181, 1993, Accessed: Jan. 06, 2026. [Online]. Available: https://books.google.com/books/about/Theory_of_Space_Plasma_Microinstabilitie.html?id=hMiulET5wpwC

P. K. . Shukla and A. A. . Mamun, “Introduction to Dusty Plasma Physics,” p. 284, 2015, Accessed: Jan. 06, 2026. [Online]. Available: https://www.researchgate.net/publication/274315867_Introduction_to_Dusty_Plasma_Physics

V. M. Vasyliunas, “A survey of low-energy electrons in the evening sector of the magnetosphere with OGO 1 and OGO 3,” J. Geophys. Res., vol. 73, no. 9, pp. 2839–2884, May 1968, doi: 10.1029/JA073I009P02839.

R. L. M. M. A. Hellberg, “Comment on ‘Mathematical and physical aspects of Kappa velocity distribution’ [Phys. Plasmas 14, 110702 (2007)],” Phys. Plasmas, vol. 16, p. 094701, 2009, doi: https://doi.org/10.1063/1.3213388.

H. S. Du, M. M. Lin, X. Gong, and W. S. Duan, “The characters of ion acoustic rogue waves in nonextensive plasma,” Phys. Plasmas, vol. 24, no. 10, Oct. 2017, doi: 10.1063/1.4996047.

T. K. B. M. A. Hellberg, “Dust acoustic solitons in plasmas with kappa-distributed electrons and/or ions,” Phys. Plasmas, vol. 15, p. 123705, 2008, doi: https://doi.org/10.1063/1.3042215.

H. A. S. W. Masood, M. N. S. Qureshi, P. H. Yoon, “Nonlinear kinetic Alfvén waves with non-Maxwellian electron population in space plasmas,” JGR Sp. Physic, 2015, doi: https://doi.org/10.1002/2014JA020459.

“Articles | Astrophysics and Space Science | Springer Nature Link.” Accessed: Mar. 23, 2026. [Online]. Available: https://link.springer.com/journal/10509/articles?page=60

L. M. Zelenyi, S. I. Popel, “Nonlinear structures in laboratory and space dusty plasmas,” Phys. D Nonlinear Phenom., vol. 481, p. 134721, 2025, doi: https://doi.org/10.1016/j.physd.2025.134721.

Huanbin Xue, Lei Zhang, “Nonlinear Wave Structures, Multistability, and Chaotic Behavior of Quantum Dust-Acoustic Shocks in Dusty Plasma with Size Distribution Effects,” Mathematics, vol. 13, no. 19, p. 3101, 2025, doi: https://doi.org/10.3390/math13193101.

B. B. Kadomtsev and V. I. Petviashvili, “On the Stability of Solitary Waves in Weakly Dispersing Media,” SPhD, vol. 15, p. 539, 1970, Accessed: Jan. 06, 2026. [Online]. Available: https://ui.adsabs.harvard.edu/abs/1970SPhD...15..539K/abstract

A. Jeffrey and T. Kakutani, “Weak Nonlinear Dispersive Waves: A Discussion Centered Around the Korteweg–De Vries Equation,” vol. 14, no. 4, pp. 582–643, Jul. 2006, doi: 10.1137/1014101.

“Nonlinear Aspects of Quantum Plasma Physics: Nanoplasmonics and Nanostructures in Dense Plasmas | Request PDF.” Accessed: Apr. 07, 2026. [Online]. Available: https://www.researchgate.net/publication/242730205_Nonlinear_Aspects_of_Quantum_Plasma_Physics_Nanoplasmonics_and_Nanostructures_in_Dense_Plasmas

J. L. Wen Xiu Ma, “A Study on Lump Solutions to a Generalized Hirota-Satsuma-Ito Equation in (2+1)-Dimensions,” Complexity, 2018, [Online]. Available: https://dl.acm.org/doi/10.1155/2018/9059858

Y. Ohta and J. Yang, “Rogue waves in the Davey-Stewartson I equation,” Phys. Rev. E, vol. 86, no. 3, p. 036604, Sep. 2012, doi: 10.1103/PhysRevE.86.036604.

M. Li, L. Wang, and F. H. Qi, “Nonlinear dynamics of a generalized higher-order nonlinear Schrödinger equation with a periodic external perturbation,” Nonlinear Dyn., vol. 86, no. 1, pp. 535–541, Oct. 2016, doi: 10.1007/S11071-016-2906-Y.

Manfred P. Leubner, “A nonextensive entropy approach to kappa distributions,” Astrophys. Space Sci., 2001, [Online]. Available: https://arxiv.org/abs/astro-ph/0111444

N. S. Alharthi, R. E. Tolba, “Turbulent, Rossby, rogue and explosive nonlinear waves in plasma at Titan’ s ionosphere,” Researchgate, 2023, [Online]. Available: https://www.researchgate.net/publication/374429331_Turbulent_Rossby_rogue_and_explosive_nonlinear_waves_in_plasma_at_Titan’_s_ionosphere

P. Chatterjee, S. Nasipuri, U. N. Ghosh, and M. R. Amin, “Nonextensive Effect on the Lump Soliton Structures in Dusty Plasma,” Springer Proc. Phys., vol. 405, pp. 123–138, 2024, doi: 10.1007/978-3-031-66874-6_10.