In view of the recent observations by plasma science-spacecraft-voyager and Cassini plasma spectrometer of Saturn's magnetosphere, the interaction between two counter-propagating ion-acoustic (IA) solitons is studied in an unmagnetized plasma consisting of warm adiabatic ions in addition to hot and cold electrons following kappa distribution. The head-on collision of the IA solitons is investigated using the extended Poincare–Lighthill–Kuo technique. Since this model supports both compressive and rarefactive solitons, therefore, the soliton collisions for both Korteweg–de Vries (KdV) and the modified KdV (mKdV) equations are investigated. The corresponding phase shifts after the collision for both these equations are also derived and examined. Furthermore, the effects of different plasma parameters (corresponding to Saturn's magnetosphere), including superthermality, density, and temperature on the colliding soliton profiles and their phase shifts, are examined. It is concluded that the phase shift is smaller when both hot and cold electrons are Maxwellian by comparison with the superthermal case.

1.
N. J.
Zabusky
and
M. D.
Kruskal
, “
Interaction of solitons in a collisionless plasma and the recurrence of initial states
,”
Phys. Rev. Lett.
15
,
240
(
1965
).
2.
H.
Poincaré
,
New Methods of Celestial Mechanics
(
NASA, TTF
,
1967
).
3.
M. J.
Lighthill
, “
A technique for rendering approximate solutions to physical problems uniformly valid
,”
London, Edinburgh Dublin Philos. Mag.
40
,
1179
(
1949
).
4.
Y.
Kuo
, “
On the flow of an incompressible viscous fluid past a flat plate at moderate Reynolds numbers
,”
J. Math. Phys.
32
,
83
(
1953
).
5.
J.-K.
Xue
, “
Head-on collision of the blood solitary waves
,”
Phys. Lett. A
331
,
409
(
2004
).
6.
S.
Li
and
W.
Duan
, “
Interactions between two solitons with an arbitrary collision direction in twodimensional Bose-Einstein condensates
,”
Eur. Phys. J. B
62
,
485
(
2008
).
7.
T.
Tsuboi
, “
Phase shift in the collision of two solitons propagating in a nonlinear transmission line
,”
Phys. Rev. A
40
,
2753
(
1989
).
8.
G.
Huang
,
S.
Lou
, and
Z.
Xu
, “
Head-on collision between two solitary waves in a Rayleigh-Bénard convecting fluid
,”
Phys. Rev. E
47
,
R3830
(
1993
).
9.
F.-G.
Wang
,
Y.-Y.
Yang
,
J.-F.
Han
, and
W.-S.
Duan
, “
Head-on collision between two solitary waves in a one-dimensional bead chain
,”
Chin. Phys. B
27
,
044501
(
2018
).
10.
A. E.
Ozden
and
H.
Demiray
, “
Re-visiting the head-on collision problem between two solitary waves in shallow water
,”
Int. J. Non-Linear Mech.
69
,
66
(
2015
).
11.
G.
Huang
and
M. G.
Velarde
, “
Head-on collision of two concentric cylindrical ion acoustic solitary waves
,”
Phys. Rev. E
53
,
2988
(
1996
).
12.
F.
Verheest
,
M. A.
Hellberg
, and
W. A.
Hereman
, “
Head-on collisions of electrostatic solitons in nonthermal plasmas
,”
Phys. Rev. E
86
,
036402
(
2012
).
13.
N.
Saini
and
K.
Singh
, “
Head-on collision of two dust ion acoustic solitary waves in a weakly relativistic multicomponent superthermal plasma
,”
Phys. Plasmas
23
,
103701
(
2016
).
14.
M.
Alam
,
M.
Hafez
,
M.
Talukder
, and
M. H.
Ali
, “
Head-on collision of ion acoustic solitary waves in electron-positron-ion nonthermal plasmas for weakly and highly relativistic regimes
,”
Phys. Plasmas
24
,
072901
(
2017
).
15.
U.
Hasan
,
W.
Masood
,
R.
Jahangir
, and
A. M.
Mirza
, “
Investigation of colliding nonlinear structures in a relativistically degenerate plasma
,”
Phys. Plasmas
25
,
072302
(
2018
).
16.
R.
Jahangir
,
S.
Ali
,
A. M.
Mirza
, and
W.
Masood
, “
Head on interaction of magnetoacoustic solitons in a spin-1/2 dense plasma with geometrical effects
,”
Phys. Scr.
94
,
125602
(
2019
).
17.
U.
Hasan
,
W.
Masood
,
R.
Jahangir
, and
A. M.
Mirza
, “
Head-on collision of nonlinear electrostatic shock waves in a relativistically degenerate plasma
,”
Phys. Scr.
95
,
015601
(
2019
).
18.
A.
Abdikian
,
S.
Vasheghani Farahani
, and
S.
Hussain
, “
The characteristics of daughter waves emerging from colliding solitary waves in astrophysical plasma media
,”
Mon. Not. R. Astron. Soc.
506
,
997
(
2021
).
19.
U.
Hasan
,
W.
Masood
,
R.
Jahangir
, and
A.
Majid Mirza
, “
Oblique interaction of electrostatic nonlinear structures in relativistically degenerate dense magnetoplasmas
,”
Contrib. Plasma Phys.
61
,
e202000208
(
2021
).
20.
R.
Jahangir
,
W.
Masood
, and
H.
Rizvi
, “
Face to face interaction of dust acoustic solitons with trapped ions
,”
Chaos, Solitons Fractals
174
,
113694
(
2023
).
21.
P.
Harvey
,
C.
Durniak
,
D.
Samsonov
, and
G.
Morfill
, “
Soliton interaction in a complex plasma
,”
Phys. Rev. E
81
,
057401
(
2010
).
22.
S.
Sharma
,
A.
Boruah
, and
H.
Bailung
, “
Head-on collision of dust-acoustic solitons in a strongly coupled dusty plasma
,”
Phys. Rev. E
89
,
013110
(
2014
).
23.
R.
Jahangir
and
W.
Masood
, “
Interaction of electron acoustic waves in the presence of superthermal electrons in terrestrial magnetosphere
,”
Phys. Plasmas
27
,
042105
(
2020
).
24.
M. Y.
Khattak
,
W.
Masood
,
R.
Jahangir
,
M.
Siddiq
,
H. A.
Alyousef
, and
S. A.
El-Tantawy
, “
Interaction of ion-acoustic solitons for multi-dimensional Zakharov Kuznetsov equation in Van Allen radiation belts
,”
Chaos, Solitons Fractals
161
,
112265
(
2022
).
25.
R.
Jahangir
,
W.
Masood
, and
H.
Rizvi
, “
Interaction of electron acoustic solitons in auroral region for an electron beam plasma system
,”
Front. Astron. Space Sci.
9
,
978314
(
2022
).
26.
M.
Shohaib
,
W.
Masood
,
H. A.
Alyousef
,
M.
Siddiq
, and
S. A.
El-Tantawy
, “
Formation and interaction of multi-dimensional electrostatic ion-acoustic solitons in two-electron temperature plasmas
,”
Phys. Fluids
34
,
093107
(
2022
).
27.
N.
Batool
,
W.
Masood
,
M.
Siddiq
,
A. W.
Alrowaily
,
S. M. E.
Ismaeel
, and
S. A.
El-Tantawy
, “
Hirota bilinear method and multi-soliton interaction of electrostatic waves driven by cubic nonlinearity in pair-ion–electron plasmas
,”
Phys. Fluids
34
,
033109
(
2023
).
28.
M. Y.
Khattak
,
W.
Masood
,
R.
Jahangir
,
M.
Siddiq
,
A. W.
Alrowaily
, and
S. A.
El-Tantawy
, “
Overtaking interaction of electron-acoustic solitons in Saturn's magnetosphere
,”
J. Low Freq. Noise Vibr. Act. Control
(published online
2023
).
29.
R.
Hirota
, “
Exact solution of the Korteweg–de Vries equation for multiple collisions of solitons
,”
Phys. Rev. Lett.
27
,
1192
(
1971
).
30.
M.
Miura
,
Bäcklund Transformation
(
Springer-Verlag
,
Berlin
,
1978
), p.
253
.
31.
V. B.
Matveev
and
M. A.
Salle
,
Darboux Transformations and Solitons
(
Springer
,
1991
).
32.
F. F.
Chen
,
Introduction to Plasma Physics and Controlled Fusion
(
Springer
,
1984
).
33.
S. A.
Alkhateeb
,
S.
Hussain
,
W.
Albalawi
,
S. A.
El-Tantawy
, and
E. I.
El-Awady
, “
Dissipative Kawahara ion-acoustic solitary and cnoidal waves in a degenerate magnetorotating plasma
,”
J. Taibah Univ. Sci.
17
,
2187606
(
2023
).
34.
S.
Raut
,
T.
Sarkar
,
P. C.
Mali
,
B. M.
Alotaibi
,
S. M. E.
Ismaeel
, and
S. A.
El-Tantawy
, “
On the propagation and interaction of ion-acoustic solitary, periodic, shock, and breather waves in a non-Maxwellian electron–positron–ion magnetoplasma
,”
Phys. Fluids
35
,
053111
(
2023
).
35.
K.
Arif
,
T.
Ehsan
,
W.
Masood
,
S.
Asghar
,
H. A.
Alyousef
,
E.
Tag-Eldin
, and
S. A.
El-Tantawy
, “
Quantitative and qualitative analyses of the mKdV equation and modeling nonlinear waves in plasma
,”
Front. Phys.
11
,
1118786
(
2023
).
36.
S. A.
El-Tantawy
,
N. A.
El-Bedwehy
,
H. N.
Abd El-Razek
, and
S.
Mahmood
, “
Large amplitude solitary waves in a warm magnetoplasma with kappa distributed electrons
,”
Phys. Plasmas
20
,
022115
(
2013
).
37.
H. A.
Alyousef
,
M.
Khalid
, and
S. A.
El-Tantawy
, “
Large amplitude electrostatic (un)modulated excitations in anisotropic magnetoplasmas: Solitons and freak waves
,”
Braz. J. Phys.
52
,
202
(
2022
).
38.
W.
Albalawi
,
S. A.
El-Tantawy
, and
S. A.
Alkhateeb
, “
The phase shift analysis of the colliding dissipative KdV solitons
,”
J. Ocean Eng. Sci.
7
,
521
(
2022
).
39.
H. A.
Alyousef
,
A. H.
Salas
,
R. T.
Matoog
, and
S. A.
El-Tantawy
, “
On the analytical and numerical approximations to the forced damped Gardner Kawahara equation and modeling the nonlinear structures in a collisional plasma
,”
Phys. Fluids
34
,
103105
(
2022
).
40.
S. A.
El-Tantawy
,
N. A.
El-Bedwehy
, and
S. K.
El-Labany
, “
Ion-acoustic super rogue waves in ultracold neutral plasmas with nonthermal electrons
,”
Phys. Plasmas
20
,
072102
(
2013
).
41.
S. A.
El-Tantawy
,
W. M.
Moslem
,
R.
Sabry
,
S. K.
El-Labany
,
M.
El-Metwally
, and
R.
Schlickeiser
, “
Head-on collision of ion-acoustic solitons in an ultracold neutral plasma
,”
Astrophys. Space Sci.
350
,
175
(
2014
).
42.
S. A.
El-Tantawy
and
T.
Aboelenen
, “
Simulation study of planar and nonplanar super rogue waves in an electronegative plasma: Local discontinuous Galerkin method
,”
Phys. Plasmas
24
,
052118
(
2017
).
43.
S.
Baboolal
,
R.
Bharuthram
, and
M.
Hellberg
, “
Cut-off conditions and existence domains for largeamplitude ion-acoustic solitons and double layers in fluid plasmas
,”
J. Plasma Phys.
44
(
1
),
1
(
1990
).
44.
T. K.
Baluku
,
M. A.
Hellberg
, and
F.
Verheest
, “
New light on ion acoustic solitary waves in a plasma with two-temperature electrons
,”
EPL
91
,
15001
(
2010
).
45.
F.
Verheest
and
W. A.
Hereman
, “
Collisions of acoustic solitons and their electric fields in plasmas at critical compositions
,”
J. Plasma Phys.
85
,
905850106
(
2019
).
46.
D.
Barbosa
and
W.
Kurth
, “
On the generation of plasma waves in Saturn's inner magnetosphere
,”
J. Geophys. Res.
98
,
9351
, https://doi.org/10.1029/93JA00477 (
1993
).
47.
D.
Young
,
J.-J.
Berthelier
,
M.
Blanc
,
J.
Burch
,
S.
Bolton
,
A.
Coates
,
F.
Crary
,
R.
Goldstein
,
M.
Grande
, and
T.
Hill
, “
Composition and dynamics of plasma in Saturn's magnetosphere
,”
Science
307
,
1262
(
2005
).
48.
P.
Schippers
,
M.
Blanc
,
N.
André
,
I.
Dandouras
,
G.
Lewis
,
L.
Gilbert
,
A.
Persoon
,
N.
Krupp
,
D.
Gurnett
, and
A.
Coates
, “
Multi-instrument analysis of electron populations in Saturn's magnetosphere
,”
J. Geophys. Res.
113
,
A07208
, https://doi.org/10.1029/2008JA013098 (
2008
).
49.
F.
Henning
,
R.
Mace
, and
S.
Pillay
, “
Electrostatic Bernstein waves in plasmas whose electrons have a dual kappa distribution: Applications to the Saturnian magnetosphere
,”
J. Geophys. Res.
116
,
A12203
, https://doi.org/10.1029/2011JA016965 (
2011
).
50.
C.
Su
and
R. M.
Mirie
, “
On head-on collisions between two solitary waves
,”
J. Fluid Mech.
98
,
509
(
1980
).
51.
J.-K.
Xue
, “
Head-on collision of dust-acoustic solitary waves
,”
Phys. Rev. E
69
,
016403
(
2004
).
52.
J.
Han
,
S.
Li
,
X.
Yang
, and
W.
Duan
, “
Head-on collision of ion-acoustic solitary waves in an unmagnetized electron-positron-ion plasma
,”
Eur. Phys. J. D
47
,
197
(
2008
).
53.
P.
Eslami
,
M.
Mottaghizadeh
, and
H. R.
Pakzad
, “
Head-on collision of ion-acoustic solitary waves in a plasma with a q-nonextensive electron velocity distribution
,”
Phys. Scr.
84
,
015504
(
2011
).
54.
U. N.
Ghosh
,
K.
Roy
, and
P.
Chatterjee
, “
Head-on collision of dust acoustic solitary waves in a four component dusty plasma with nonthermal ions
,”
Phys. Plasmas
18
,
103703
(
2011
).
55.
U. N.
Ghosh
,
P.
Chatterjee
, and
R.
Roychoudhury
, “
The effect of q-distributed electrons on the head-on collision of ion acoustic solitary waves
,”
Phys. Plasmas
19
,
012113
(
2012
).
56.
S. A.
El-Tantawy
and
W. M.
Moslem
, “
Nonlinear structures of the Korteweg-de Vries and modified Korteweg-de Vries equations in non-Maxwellian electron-positron-ion plasma: Solitons collision and rogue waves
,”
Phys. Plasmas
21
,
052112
(
2014
).
57.
S. A.
El-Tantawy
, “
Nonlinear dynamics of soliton collisions in electronegative plasmas: The phase shifts of the planar KdV- and mkdV-soliton collisions
,”
Chaos, Solitons Fractals
93
,
162
(
2016
).
58.
T.
Baluku
and
M.
Hellberg
, “
Ion acoustic solitons in a plasma with two-temperature kappa-distributed electrons
,”
Phys. Plasmas
19
,
012106
(
2012
).
59.
K.
Annou
, “
Ion-acoustic solitons in plasma: An application to Saturn's magnetosphere
,”
Astrophys. Space Sci.
357
,
163
(
2015
).
You do not currently have access to this content.