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Instability and interaction of the nonlinear solitary waves in two-temperature-ion dusty plasma

Zhong Sheng-Ren

Instability and interaction of the nonlinear solitary waves in two-temperature-ion dusty plasma

Zhong Sheng-Ren
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  • For nonlinear dust acoustic waves in unmagnetized dusty plasma containing cold dust grains and isothermal electrons and ions, small but finite amplitude nonlinear waves are governed by the Korteweg de Veries (KdV) equation. For weakly two-dimensional dust acoustic solitary waves in a dusty plasma with variable dust charge and two-temperature ions, we obtain a Kadomtsev-Petviashvili equation under higher order transverse disturbances for this system. The interactions between two solitons and three solitons propagating in arbitrary directions are investigated. It is found that the maximum amplitude in the interaction region between two same——amplitude solitons is about four times that of a single soliton, while for three solitons the maximum amplitude is nine times that of a single soliton. It suggests that the transverse perturbations for the weakly nonlinear solitary waves in dusty plasma with variable dust charge and two-temperature ions are stable.
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    [1]Rao N N,Shukla P K,Yu M Y 1990 Planet. Space Sci. 38 543

    [2]

    [2]Shukla P K,Silin V P 1992 Phys. Script. 45 508

    [3]

    [3]D′Angelo N 1990 Planet. Space Sci. 38 1143

    [4]

    [4]Goertz C K 1989 Rev. Geophys. 27 271

    [5]

    [5]Verheest F 1996 Space Sci. Rev. 77 267

    [6]

    [6]Chu J H,Du J B,Lin I H 1994 J. Phys. D 27 296

    [7]

    [7]D′Angelo N 1995 J. Phys. D 28 1009[8]Barkan A,Merlino R L,D′Angelo N 1995 Phys. Plasma. 2 3563

    [8]

    [9]Barkan A,Merlino R L,D′Angelo N 1996 Planet. Space Sci. 44 239

    [9]

    ]Duan W S,Shi Y R 2003 Chaos, Solitons Fract. 18 321

    [10]

    ]Duan W S,Parkes J,Lin M M 2005 Phys. Plasmas 12 022106

    [11]

    ]Chen J H,Duan W S 2007 Phys. Plasmas 14 083702

    [12]

    ]Meuris P 1997 Planet. Space Sci. 45 449

    [13]

    ]Meuris P 1997 Space Sci. 45 1171

    [14]

    ]Han J N,Yang X X,Tiao T X,Duan WS 2008 Phys. Lett. A 372 4817

    [15]

    ]Li S C,Han J N,Duan WS 2009 Physica B 404 1235

    [16]

    ]Han J N,Du S L,Duan W S 2008 Phys. Plasmas 15 112104

    [17]

    ]Han J N,Duan W S,Li S C,Wang C L 2008 Acta Phys. Sin. 57 6068 (in Chinese) [韩久宁、段文山、栗生长、王苍龙 2008 物理学报 57 6068]

    [18]

    ]He G J,TianD X,Lin M M,Duan W S 2008 Acta Phys. Sin. 57 2320 (in Chinese) [何广军、田多祥、林麦麦、段文山 2008 物理学报 57 2320]

    [19]

    ]Jiang X,Gao Y X, Li S C, Shi Y R,Duan WS 2009 Appl. Math. Comp. 214 60

    [20]

    ]Yang X X,Duan W S,Han J N,Li S C 2008 Chin. Phys. B 17 2985

  • [1]

    [1]Rao N N,Shukla P K,Yu M Y 1990 Planet. Space Sci. 38 543

    [2]

    [2]Shukla P K,Silin V P 1992 Phys. Script. 45 508

    [3]

    [3]D′Angelo N 1990 Planet. Space Sci. 38 1143

    [4]

    [4]Goertz C K 1989 Rev. Geophys. 27 271

    [5]

    [5]Verheest F 1996 Space Sci. Rev. 77 267

    [6]

    [6]Chu J H,Du J B,Lin I H 1994 J. Phys. D 27 296

    [7]

    [7]D′Angelo N 1995 J. Phys. D 28 1009[8]Barkan A,Merlino R L,D′Angelo N 1995 Phys. Plasma. 2 3563

    [8]

    [9]Barkan A,Merlino R L,D′Angelo N 1996 Planet. Space Sci. 44 239

    [9]

    ]Duan W S,Shi Y R 2003 Chaos, Solitons Fract. 18 321

    [10]

    ]Duan W S,Parkes J,Lin M M 2005 Phys. Plasmas 12 022106

    [11]

    ]Chen J H,Duan W S 2007 Phys. Plasmas 14 083702

    [12]

    ]Meuris P 1997 Planet. Space Sci. 45 449

    [13]

    ]Meuris P 1997 Space Sci. 45 1171

    [14]

    ]Han J N,Yang X X,Tiao T X,Duan WS 2008 Phys. Lett. A 372 4817

    [15]

    ]Li S C,Han J N,Duan WS 2009 Physica B 404 1235

    [16]

    ]Han J N,Du S L,Duan W S 2008 Phys. Plasmas 15 112104

    [17]

    ]Han J N,Duan W S,Li S C,Wang C L 2008 Acta Phys. Sin. 57 6068 (in Chinese) [韩久宁、段文山、栗生长、王苍龙 2008 物理学报 57 6068]

    [18]

    ]He G J,TianD X,Lin M M,Duan W S 2008 Acta Phys. Sin. 57 2320 (in Chinese) [何广军、田多祥、林麦麦、段文山 2008 物理学报 57 2320]

    [19]

    ]Jiang X,Gao Y X, Li S C, Shi Y R,Duan WS 2009 Appl. Math. Comp. 214 60

    [20]

    ]Yang X X,Duan W S,Han J N,Li S C 2008 Chin. Phys. B 17 2985

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  • Received Date:  19 July 2009
  • Accepted Date:  17 August 2009
  • Published Online:  15 April 2010

Instability and interaction of the nonlinear solitary waves in two-temperature-ion dusty plasma

  • 1. 武威职业学院工程技术系,武威 733000

Abstract: For nonlinear dust acoustic waves in unmagnetized dusty plasma containing cold dust grains and isothermal electrons and ions, small but finite amplitude nonlinear waves are governed by the Korteweg de Veries (KdV) equation. For weakly two-dimensional dust acoustic solitary waves in a dusty plasma with variable dust charge and two-temperature ions, we obtain a Kadomtsev-Petviashvili equation under higher order transverse disturbances for this system. The interactions between two solitons and three solitons propagating in arbitrary directions are investigated. It is found that the maximum amplitude in the interaction region between two same——amplitude solitons is about four times that of a single soliton, while for three solitons the maximum amplitude is nine times that of a single soliton. It suggests that the transverse perturbations for the weakly nonlinear solitary waves in dusty plasma with variable dust charge and two-temperature ions are stable.

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