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研究了小的有限振幅的无磁场尘埃等离子体中的非线性波.在一维情况下由Korteweg de Veries (KdV)方程来描述，考虑了二维情况下尘埃等离子体中尘埃颗粒上电荷的变化效应以及双温度离子效应后，尘埃等离子体受到横向高阶扰动后动力学方程由Kadomtsev-Petviashvili(KP)方程来描述.在此基础上，研究了以任意夹角传播的两个及三个孤立子的相互作用问题，考虑非线性效应后振幅相等的双孤立子在相互作用区域内振幅最大值是单个孤立子振幅的4倍，振幅相等的三孤立子在相互作用区域内振幅最大值是单个孤立子振幅的9倍.研究还表明波的传播方向受到横向高阶扰动后是稳定的.
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关键词:
- 尘埃等离子体 /
- 稳定性 /
- Kadomtsev-Petviashvili方程
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.-
Keywords:
- dusty plasmas /
- instability /
- Kadomtsev-Petviashvili equation
[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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[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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