Weakly relativistic effect in the formation of ion-acoustic solitary waves in a positive ion-beam plasma
Relativistic solitons are investigated in a plasma with positive-ion beams using the Korteweg-de Vries (KdV) equation considering relativistic effects smaller for i O(v 2 /c 2 ) and e O(u 2 /c 2 ), and larger for i O(v 4 /c 4 ) and e O(u 4 /c 4 ), where γ i = { 1 − ( v c ) 2 } − ( 1 / 2 ) and γ e...
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| Published in | Canadian journal of physics Vol. 88; no. 3; pp. 157 - 164 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Ottawa
NRC Research Press
01.03.2010
Canadian Science Publishing NRC Research Press |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0008-4204 1208-6045 |
| DOI | 10.1139/P10-008 |
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| Abstract | Relativistic solitons are investigated in a plasma with positive-ion beams using the Korteweg-de Vries (KdV) equation considering relativistic effects smaller for
i
O(v
2
/c
2
) and
e
O(u
2
/c
2
), and larger for
i
O(v
4
/c
4
) and
e
O(u
4
/c
4
), where
γ
i
=
{
1
−
(
v
c
)
2
}
−
(
1
/
2
)
and
γ
e
=
{
1
−
(
u
c
)
2
}
−
(
1
/
2
)
are relativistic factors of positive ions and electrons, respectively. Only compressive solitons of reasonable amplitudes are established subject to a mathematical condition in terms of initial and physical parameters with fourth-order terms in
β
i
0
′
=
1
+
3
v
0
2
2
c
2
+
15
v
0
4
8
c
4
and
β
e
0
′
=
1
+
3
u
0
2
2
c
2
+
15
u
0
4
8
c
4
for higher order relativistic effects and lower order relativistic effects without fourth-order terms in
β
i
0
′
and
β
e
0
′
for Q′ < 1 and Q′ > 1. The role of positive ion beams in a plasma with higher and lower order relativistic effects in the formation of relativistic solitons is fully explored in the investigation. |
|---|---|
| AbstractList | Relativistic solitons are investigated in a plasma with positive-ion beams using the Korteweg-de Vries (KdV) equation considering relativistic effects smaller for [γ.sub.i] ≅ O([v.sup.2]/[c.sup.2]) and [γ.sub.e] ≅ O([u.sup.2]/[c.sup.2]), and larger for [γ.sub.i] [approximately equal to] O([v.sup.4]/[c.sup.4]) and [γ.sub.e] ≅ O([u.sup.4]/[c.sup.4]), where [γ.sub.i] = [{1 - [(v/c).sup.2]}.sup.- (1/2)] and [γ.sub.e] = [{1 - [(u/c).sup.2]}.sup.-(1/2)] are relativistic factors of positive ions and electrons, respectively. Only compressive solitons of reasonable amplitudes are established subject to a mathematical condition in terms of initial and physical parameters with fourth-order terms in [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] for higher order relativistic effects and lower order relativistic effects without fourth-order terms in [β.sup.'.sub.i0] and [β.sup.'.sub.e0] for [Q.sup.'] < 1 and [Q.sup.'] > 1. The role of positive ion beams in a plasma with higher and lower order relativistic effects in the formation of relativistic solitons is fully explored in the investigation. Relativistic solitons are investigated in a plasma with positive-ion beams using the Korteweg-de Vries (KdV) equation considering relativistic effects smaller for ... O(v.../c...) and ... Ou.../c...), and larger for ... O(v.../c...) and ... O(u.../c...), where ... and ... are relativistic factors of positive ions and electrons, respectively. Only compressive solitons of reasonable amplitudes are established subject to a mathematical condition in terms of initial and physical parameters with fourth-order terms in ... and ... for higher order relativistic effects and lower order relativistic effects without fourth-order terms in ... and ... for ... < 1 and ... > 1. The role of positive ion beams in a plasma with higher and lower order relativistic effects in the formation of relativistic solitons is fully explored in the investigation. (ProQuest: ... denotes formulae/symbols omitted.) Relativistic solitons are investigated in a plasma with positive-ion beams using the Korteweg-de Vries (KdV) equation considering relativistic effects smaller for g(i) ≈ O(v(2)/c(2)) and g(e) ≈ O(u(2)/c(2)), and larger for g(i) ≈ O(v(4)/c(4)) and g(e) ≈ O(u(4)/c(4)), where and are relativistic factors of positive ions and electrons, respectively. Only compressive solitons of reasonable amplitudes are established subject to a mathematical condition in terms of initial and physical parameters with fourth-order terms in and for higher order relativistic effects and lower order relativistic effects without fourth-order terms in and for Q' < 1 and Q' > 1. The role of positive ion beams in a plasma with higher and lower order relativistic effects in the formation of relativistic solitons is fully explored in the investigation. PACS No.: 52.35.-g Relativistic solitons are investigated in a plasma with positive-ion beams using the Korteweg-de Vries (KdV) equation considering relativistic effects smaller for [γ.sub.i] ≅ O([v.sup.2]/[c.sup.2]) and [γ.sub.e] ≅ O([u.sup.2]/[c.sup.2]), and larger for [γ.sub.i] [approximately equal to] O([v.sup.4]/[c.sup.4]) and [γ.sub.e] ≅ O([u.sup.4]/[c.sup.4]), where [γ.sub.i] = [{1 - [(v/c).sup.2]}.sup.- (1/2)] and [γ.sub.e] = [{1 - [(u/c).sup.2]}.sup.-(1/2)] are relativistic factors of positive ions and electrons, respectively. Only compressive solitons of reasonable amplitudes are established subject to a mathematical condition in terms of initial and physical parameters with fourth-order terms in [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] for higher order relativistic effects and lower order relativistic effects without fourth-order terms in [β.sup.'.sub.i0] and [β.sup.'.sub.e0] for [Q.sup.'] < 1 and [Q.sup.'] > 1. The role of positive ion beams in a plasma with higher and lower order relativistic effects in the formation of relativistic solitons is fully explored in the investigation. PACS No: 52.35.-g Nous avons etudiee des solitons relativistes dans un plasma traverse; par des faisceaux d'ions positifs, a l'aide de l'equation de Korteweg-de Vries (KdV), pour des effets relativistes faibles avec [γ.sub.i] ≅ O([v.sup.2]/[c.sup.2]) et [γ.sub.e] ≅ O([u.sup.2]/[c.sup.2]), ainsi que des effets forts avec [γ.sub.i] ≅ O([v.sup.4]/[c.sup.4]) et [γ.sub.e] ≅ O([u.sup.4]/[c.sup.4]), la ou [γ.sub.i] = [{1 - [(v/c).sup.2]}.sup.-(1/2)] et [γ.sub.e] = [{1 - [(u/c).sup.2]}.sup.-(1/2)] sont les facteurs relativistes des ions positifs et des electrons respectivement. Seuls des solitons de compression d'amplitude raisonnable emergent, sujets a des conditions mathematiques fonctions de parametres initiaux et physiques pour des effets forts avec des parametres du quatrieme ordre en [EXPRESSION MATHEMATIQUE NON REPRODUCTIBLE EN ASCII.] et [EXPRESSION MATHEMATIQUE NON REPRODUCTIBLE EN ASCII.] et des effets faibles sans termes du quatrieme ordre dans [β.sup.'.sub.i0] et [β.sup.'.sub.e0] pour [Q.sup.'] <1 et [Q.sup.'] > 1. Nous faisons une etude complete du role du faisceau d'ions positifs dans le plasma, avec des effets relativistes faibles et forts, dans la formation des solitons relativistes. [Traduit par la Redaction] Relativistic solitons are investigated in a plasma with positive-ion beams using the Korteweg–de Vries (KdV) equation considering relativistic effects smaller for γ i ≈ O(v 2 /c 2 ) and γ e ≈ O(u 2 /c 2 ), and larger for γ i ≈ O(v 4 /c 4 ) and γ e ≈ O(u 4 /c 4 ), where [Formula: see text] and [Formula: see text] are relativistic factors of positive ions and electrons, respectively. Only compressive solitons of reasonable amplitudes are established subject to a mathematical condition in terms of initial and physical parameters with fourth-order terms in [Formula: see text] and [Formula: see text] for higher order relativistic effects and lower order relativistic effects without fourth-order terms in [Formula: see text] and [Formula: see text] for Q′ < 1 and Q′ > 1. The role of positive ion beams in a plasma with higher and lower order relativistic effects in the formation of relativistic solitons is fully explored in the investigation. Relativistic solitons are investigated in a plasma with positive-ion beams using the Korteweg-de Vries (KdV) equation considering relativistic effects smaller for i O(v 2 /c 2 ) and e O(u 2 /c 2 ), and larger for i O(v 4 /c 4 ) and e O(u 4 /c 4 ), where γ i = { 1 − ( v c ) 2 } − ( 1 / 2 ) and γ e = { 1 − ( u c ) 2 } − ( 1 / 2 ) are relativistic factors of positive ions and electrons, respectively. Only compressive solitons of reasonable amplitudes are established subject to a mathematical condition in terms of initial and physical parameters with fourth-order terms in β i 0 ′ = 1 + 3 v 0 2 2 c 2 + 15 v 0 4 8 c 4 and β e 0 ′ = 1 + 3 u 0 2 2 c 2 + 15 u 0 4 8 c 4 for higher order relativistic effects and lower order relativistic effects without fourth-order terms in β i 0 ′ and β e 0 ′ for Q′ < 1 and Q′ > 1. The role of positive ion beams in a plasma with higher and lower order relativistic effects in the formation of relativistic solitons is fully explored in the investigation. |
| Abstract_FL | Nous avons étudié des solitons relativistes dans un plasma traversé par des faisceaux d'ions positifs, à l'aide de l'équation de Korteweg-de Vries (KdV), pour des effets relativistes faibles avec
i
O(v
2
/c
2
) et
e
O(u
2
/c
2
), ainsi que des effets forts avec
i
O(v
4
/c
4
) et
e
O(u
4
/c
4
), là où
γ
i
=
{
1
−
(
v
c
)
2
}
−
1
/
2
et
γ
e
=
{
1
−
(
u
c
)
2
}
−
1
/
2
sont les facteurs relativistes des ions positifs et des électrons respectivement. Seuls des solitons de compression d'amplitude raisonnable émergent, sujets à des conditions mathématiques fonctions de paramètres initiaux et physiques pour des effets forts avec des paramètres du quatrième ordre en
β
i
0
′
=
1
+
3
v
0
2
2
c
2
+
15
v
0
4
8
c
4
et
β
e
0
′
=
1
+
3
u
0
2
2
c
2
+
15
u
0
4
8
c
4
et des effets faibles sans termes du quatrième ordre dans
β
i
0
′
et
β
e
0
′
pour Q′ < 1 et Q′ > 1. Nous faisons une étude complète du rôle du faisceau d'ions positifs dans le plasma, avec des effets relativistes faibles et forts, dans la formation des solitons relativistes. |
| Audience | Academic |
| Author | Das, R. Sarmah, H. K. Kalita, B. C. |
| Author_xml | – sequence: 1 givenname: B. C. surname: Kalita fullname: Kalita, B. C. organization: Department of Mathematics, Gauhati University, Guwahati - 781014, Assam, India – sequence: 2 givenname: R. surname: Das fullname: Das, R. email: ranjan_ghy@sify.com organization: Department of Mathematics, Arya Vidyapeeth College, Guwahati - 781016, Assam, India – sequence: 3 givenname: H. K. surname: Sarmah fullname: Sarmah, H. K. organization: Department of Mathematics, Gauhati University, Guwahati - 781014, Assam, India |
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| Cites_doi | 10.1063/1.865050 10.1063/1.870614 10.1063/1.1894398 10.1088/0032-1028/20/6/006 10.1007/s10582-006-0455-1 10.1017/S0022377800012976 10.1017/S0022377800018158 10.1103/PhysRevLett.17.996 10.1063/1.859906 10.1088/0032-1028/19/10/002 10.1063/1.3123423 10.1088/0032-1028/22/8/006 10.1088/0305-4470/19/17/020 10.1103/PhysRevLett.34.77 10.1063/1.1695558 10.1016/j.physleta.2006.09.053 10.1063/1.3050061 10.1017/S0022377800015117 10.1017/S0022377806005344 10.1016/0375-9601(79)90281-0 10.1017/S0022377800012320 10.1088/0032-1028/23/7/006 10.1143/JPSJ.71.2918 10.1063/1.2750650 10.1017/S0022377800017190 10.1063/1.859946 |
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| References | rg1/ref1 rg23/ref23 rg21/ref21 rg19/ref19 rg12/ref12 rg16/ref16 rg18/ref18 Abrol P.S. (rg3/ref3) 1979; 75 rg27/ref27 rg10/ref10 rg4/ref4 rg7/ref7 rg22/ref22 rg13/ref13 Gill T.S. (rg24/ref24) 2007; 361 rg9/ref9 rg6/ref6 rg11/ref11 rg15/ref15 rg26/ref26 rg17/ref17 rg8/ref8 rg25/ref25 rg5/ref5 Ostrovskii L.A. (rg2/ref2) 1976; 42 rg20/ref20 rg14/ref14 |
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| Snippet | Relativistic solitons are investigated in a plasma with positive-ion beams using the Korteweg-de Vries (KdV) equation considering relativistic effects smaller... Relativistic solitons are investigated in a plasma with positive-ion beams using the Korteweg–de Vries (KdV) equation considering relativistic effects smaller... |
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| SubjectTerms | 52.35.-g Effects Electrons High temperature plasmas Ion bombardment Physics Plasma Plasma (Ionized gases) Properties Solitary waves Solitons Waves |
| Title | Weakly relativistic effect in the formation of ion-acoustic solitary waves in a positive ion-beam plasma |
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