Bäcklund transformation and multiple soliton solutions for a cylindrical KdV equation to model electron-acoustic waves in the Saturnian magnetosphere
Source abstract
Abstract
In this work, we investigate nonlinear electron-acoustic waves (EAWs) in the Saturn’s magnetosphere, modeled as a plasma system with cold inertial electrons, inertia-less kappa-distributed hot electrons, and stationary ions. Using the reductive perturbation technique, the cylindrical Korteweg–de Vries (CKdV) equation for small-amplitude EAWs is derived. The Bäcklund transformation is employed to analyze the CKdV equation. This approach yields novel analytical multi-soliton solutions in terms of Airy functions, with a recursive scheme for N-soliton solutions. Parametric analysis using Cassini data shows that only rarefactive solitary waves are supported for the system of interest. The impact of related plasma parameters on the profile of the cylindrical electron-acoustic soliton is numerically examined. These results elucidate nonlinear electrostatic structure formation in the planetary magnetospheres and provide a framework for interpreting spaceborne data.
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Research context
OpenAlex topics: Dust and Plasma Wave Phenomena · Ionosphere and magnetosphere dynamics · Astro and Planetary Science
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Department of Physics, COMSATS University Islamabad 1 , Islamabad,
National Center for Physics (NCP), Quaid-i-Azam University Campus 2 , Shahdrah Valley Road, Islamabad 44000,
Department of Physics, College of Science, Princess Nourah Bint Abdulrahman University 3 , P.O. Box 84428, Riyadh 11671,
Department of Mathematics, Chittagong University of Engineering & Technology 4 , Chattogram 4349,
Funding
Princess Nourah Bint Abdulrahman University
References (53)
Show source-provided references
1. Longitudinal ion oscillations in a hot plasma10.1063/1.1706174 ↗
2. Electrostatic hiss and the beam driven electron acoustic instability in the dayside polar cusp10.1029/gl011i012p01180 ↗
3. Electron-acoustic mode in a plasma of two-temperature electrons10.1143/jpsj.43.1819 ↗
4. Electron-acoustic solitons in an electron-beam plasma system10.1063/1.874150 ↗
5. Propagation of electronic longitudinal modes in a non-Maxwellian plasma10.1017/s0022377800007169 ↗
6. Generation of broadband electrostatic noise by electron acoustic solitons10.1029/90gl02677 ↗
7. Modulated electron-acoustic waves in auroral density cavities: FAST observations10.1029/1999gl900462 ↗
8. Isolated electrostatic structures observed throughout the cluster orbit: Relationship to magnetic field strength10.5194/angeo-22-2515-2004 ↗
9. Comparisons of polar satellite observations of solitary wave velocities in the plasma sheet boundary and the high altitude cusp to those in the auroral zone10.1029/1998gl900304 ↗
10. FAST satellite observations of large-amplitude solitary structures10.1029/98gl00636 ↗
11. Simulation studies on the dissipative modified Kawahara solitons in a complex plasma10.3390/sym15010057 ↗
12. A survey of low-energy electrons in the evening sector of the magnetosphere with OGO 1 and OGO 310.1029/ja073i009p02839 ↗
13. Fundamental issues on kappa-distributions in space plasmas and interplanetary proton distributions10.1063/1.1667501 ↗
14. Multi-instrument analysis of electron populations in Saturn’s magnetosphere10.1029/2008JA013098 ↗
15. Electron acoustic waves in double-kappa plasmas: Application to Saturn’s magnetosphere10.1029/2010ja016112 ↗
16. Electron acoustic solitary waves with kappa-distributed electrons10.1088/0031-8949/84/02/025507 ↗
17. Oblique modulation and envelope excitations of nonlinear ion sound waves with cubic nonlinearity and generalized (r, q) distribution10.1088/1402-4896/ab346e ↗
18. Propagation of ion-acoustic solitary waves of small amplitude10.1103/physrevlett.17.996 ↗
19. Propagation of two-solitons in an electron acoustic waves in a plasma with electrons featuring Tsallis distribution10.1007/s10509-013-1467-5 ↗
20. Interaction of electron acoustic waves in the presence of superthermal electrons in terrestrial magnetosphere10.1063/1.5143400 ↗
21. On the analytical and numerical solutions of the damped nonplanar Shamel Korteweg–de Vries Burgers equation for modeling nonlinear structures in strongly coupled dusty plasmas: Multistage homotopy perturbation method10.1063/5.0040886 ↗
22. Cylindrical solitons10.1063/1.1694941 ↗
23. Bäcklund transformation for analyzing a cylindrical Korteweg–de Vries equation and investigating multiple soliton solutions in a plasma10.1063/5.0166075 ↗
24. Bäcklund transformation of the cylindrical KdV equation10.1143/jpsj.49.2380 ↗
25. Exact solution of the Korteweg—de Vries equation for multiple collisions of solitons10.1103/physrevlett.27.1192 ↗
26. Bäcklund transformation for solutions of the Korteweg–de Vries equation10.1103/physrevlett.31.1386 ↗
27. 1991
28. Solitary potentials in cometary dusty plasmas10.1029/2002GL015219 ↗
29. 2015
30. Observations of ion-acoustic cylindrical solitons10.1103/physrevlett.32.581 ↗
31. The Miura transform and the existence of an infinite number of conservation laws of the cylindrical KdV equation10.1016/0375-9601(81)90924-5 ↗
32. The Painlevé property for partial differential equations10.1063/1.525721 ↗
33. Symbolic software for the painlevé test of nonlinear ordinary and partial differential equations10.2991/jnmp.2006.13.1.8 ↗
34. On the multi-solitons interaction, shock waves, and hybrid solutions to the variable coefficients perturbed damped modified Korteweg–de Vries–Zakharov–Kuznetsov equation arising in plasma and fluids10.59277/romrepphys.2025.77.122 ↗
35. Nonlinear drift waves and their role in Saturn’s B-ring: Implications of rotation-induced dispersive dust drift waves and plasma parameter effects on spokes10.1016/j.rinp.2025.108149 ↗
36. Nonlinear ion acoustic waves in dense magnetoplasmas: Analyzing interaction solutions of the KdV equation using Wronskian formalism for electron trapping with Landau diamagnetism and thermal excitations10.1016/j.chaos.2024.114638 ↗
37. Overtaking interaction of electron-acoustic solitons in Saturn’s magnetosphere10.1177/14613484231189636 ↗
38. Modulational instability and associated multiple dark solitons in relativistically degenerate electron-positron-ion plasmas10.1038/s41598-025-10607-9 ↗
39. Interaction of nonlinear acoustic waves in dusty plasma with Cairns–Gurevich polarization force10.1007/s11082-025-08437-0 ↗
40. Exploring the dynamics of overtaking interactions of electron acoustic solitons in beam-driven unmagnetized plasmas: Application in the auroral region10.1088/1402-4896/ad9bf9 ↗
41. Effect of adiabatic trapping of electrons on the nonlinear evolution of ion temperature gradient driven drift mode in a dispersive plasma10.1088/1402-4896/ad68da ↗
42. Hirota bilinear method and multi-soliton interaction of electrostatic waves driven by cubic nonlinearity in pair-ion–electron plasmas10.1063/5.0142447 ↗
43. Electron-acoustic (un)modulated structures in a plasma having (r, q)-distributed electrons: Solitons, super rogue waves, and breathers10.3390/sym13112029 ↗
44. Interaction of two-dimensional electron-acoustic solitary waves in a cylindrical geometry and their applications in space plasmas10.1063/5.0220184 ↗
45. Investigation of nonlinear cylindrical electrostatic excitations in dense quantum astrophysical plasmas10.1007/s13538-024-01655-z ↗
46. The attributes of the dust-acoustic solitary and periodic structures in the Saturn’s inner magnetosphere10.1063/5.0137784 ↗
47. On the “Tantawy Technique” and other methods for analyzing the family of fractional Burgers’ equations: Applications to plasma physics10.1177/14613484251314580 ↗
48. Novel approximations to the fourth-order fractional Cahn–Hillard equations: Application to the Tantawy technique and other two techniques with Yang transform10.1177/14613484251322240 ↗
49. Application of the Tantawy technique for modeling fractional ion-acoustic waves in electronegative plasmas having Cairns distributed-electrons, part (I): Fractional KdV solitary waves10.1007/s13538-025-01741-w ↗
50. Application of the tantawy technique for modeling fractional ion-acoustic waves in electronegative nonthermal plasmas, part (II): Fractional modified KdV-solitary waves10.1007/s13538-025-01800-2 ↗
51. Novel approximations to the multi-dimensional fractional diffusion models using the tantawy technique and two other transformed methods10.3390/fractalfract9070423 ↗
52. On the tantawy technique for analyzing (in)homogeneous fractional physical wave equations10.1007/s11227-025-07868-6 ↗
53. Modeling fractional dust-acoustic shock waves in a complex plasma using novel techniques10.3390/fractalfract9100674 ↗