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The stability of solitay wave solution to a modified Kadomtsev-Petviashvili equation

Zhang Juan Zhou Zhi-Gang Shi Yu-Ren Yang Hong-Juan Duan Wen-Shan

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The stability of solitay wave solution to a modified Kadomtsev-Petviashvili equation

Zhang Juan, Zhou Zhi-Gang, Shi Yu-Ren, Yang Hong-Juan, Duan Wen-Shan
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  • The reductive perturbation method is employed to describe the behaviour of ion-acoustic waves for plasmas in the absence of magnetic field, leading to a type of modified Kadomtsev-Petviashvili equation. The stability of a special type of solitary wave solutions for the modified Kadomtsev-Petviashvili equation is investigated with a finite difference scheme. The numerical results show that this solitary wave is unstable under two particular initial perturbations.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11047010), the Key Project Foundation of the Education Ministry of China (Grant No. 209128), and the Natural Science Foundation of Northwest Normal University (Grant No. NWNU-KJCXGC-03-53).
    [1]

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

    [2]

    Shukla P K, Silin V P 1992 Phys. Scr. 45 508

    [3]

    Wei L, Wang Y N 2007 Phys. Rev. B 75 193407

    [4]

    He B G, Xu C Z, Zhang J F 2006 Acta Phys. Sin. 55 511 (in Chinese) [何宝钢, 徐昌智, 张解放 2006 物理学报 55 511]

    [5]

    Hou L J, Wang Y N, Miskovic Z L 2004 Phys. Rev. E 70 056406

    [6]

    Ma S H, Wu X H, Fang J P, Zheng C L 2008 Acta Phys. Sin. 57 11 (in Chinese) [马松华, 吴小红, 方建平, 郑春龙 2008 物理学报 57 11]

    [7]

    Xie B S, Du S C 2006 Phys. Plasmas 13 074504

    [8]

    Xie B S, Li H B, Hu B B 2005 Eur. Phys. Lett. 69 358

    [9]

    Xie B S, Wang N C 2002 Phys. Scr. 65 444

    [10]

    Xie B S, Yu M Y 2000 Phys. Plasmas 7 3137

    [11]

    Xie B S, He K F, Huang Z Q, 2000 Chin. Phys. Lett. 17 815

    [12]

    Xie B S, He K F, Huang Z Q 1999 Phys. Plasmas 6 3808

    [13]

    Huang G X, Velarde M G, Makrov V A 2001 Phys. Rev. A 64 013617

    [14]

    Duan W S 2004 Chin. Phys. 13 598

    [15]

    Duan W S 2004 Chaos, Solitons and Fractals 21 319

    [16]

    Mao J J, Yang J R 2007 Acta Phys. Sin. 56 5049 (in Chinese) [毛杰健, 杨建荣 2007 物理学报 56 5049]

    [17]

    Lu D C, Hong B J, Tian L X 2006 Acta Phys. Sin. 55 5617 (in Chinese) [卢殿臣, 洪宝剑, 田立新 2006 物理学报 55 5617]

    [18]

    Han J N, Li S C, Yang X X, Duan W S 2008 Eur. Phys. J. D 47 197

    [19]

    Mushtaq A, Khan S A 2007 Phys. Plasmas 14 052307

    [20]

    Xiao D L, Ma J X, Li Y F, Xia Y H, Yu M Y 2006 Phys. Plasmas 13 052308

    [21]

    Goerts C K 1998 Rev. Geophys. 27 271

    [22]

    Havnes O, Melandse F, La Hoz C, Aslaksen T K, Hartquist T 1992 Phys. Scr. 45 433

    [23]

    Benkadda S, Tsytovich V N, Verga A 1995 Comments Plasmas Phys. Cont. Fus. 16 321

    [24]

    Verheest F 1996 Space Sci. Rev. 77 267

    [25]

    Shukla P K, Silin V P, Yu My 1992 Phys. Scr. 45 508

    [26]

    Barkar A, Meclino R L, D'Angelo N 1995 Phys. Plasma 2 3563

    [27]

    Morfill G E, Thomos H 1996 J. Vac. Sci. Technol. A 14 490

    [28]

    Merlino R L, Barkan A, Thompson C, D'Angelo N 1990 Plant Space Sci. 38 1143

    [29]

    Duan W S 2001 Phys. Plasmas 8 3583

    [30]

    Hong X R, Duan W S, Song J A, Shi Y R, Lü K P 2003 Acta Phys. Sin. 52 2671 (in Chinese) [洪学仁, 段文山, 孙建安, 石玉仁, 吕克璞 2003 物理学报 52 2671]

    [31]

    Shi Y R, Zhang J, Yang H J, Duan W S 2011 Acta Phys. Sin. 60 020402 (in Chinese) [石玉仁, 张娟, 杨红娟, 段文山 2011 物理学报 60 020402]

    [32]

    Shi Y R, Zhang J, Yang H J, Duan W S, Karl E Lonngren 2011 Chin. Phys. B 20 015205

    [33]

    Das J, Bandyopadhyay A, Das K P 2007 Phys. Plasmas 14 092403

    [34]

    Singh D K, Malik H K 2007 Plasma Phys. Contr. F 49 1551

    [35]

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

    [36]

    Han J N, Yang X X, Tian D X, Duan W S 2008 Phys. Lett. A 372 4817

    [37]

    Tian B, Gao Y T 2007 Phys. Lett. A 362 283

    [38]

    Duan W S, Hong X R 2003 Acta Phys. Sin. 52 1337 (in Chinese) [段文山, 洪学仁 2003 物理学报 52 1337]

    [39]

    Ikezi H, Taylor R J, Baker D R 1970 Phys. Rev. Lett. 25 11

    [40]

    Schamel H 1973 Phys. Plasmas 9 377

  • [1]

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

    [2]

    Shukla P K, Silin V P 1992 Phys. Scr. 45 508

    [3]

    Wei L, Wang Y N 2007 Phys. Rev. B 75 193407

    [4]

    He B G, Xu C Z, Zhang J F 2006 Acta Phys. Sin. 55 511 (in Chinese) [何宝钢, 徐昌智, 张解放 2006 物理学报 55 511]

    [5]

    Hou L J, Wang Y N, Miskovic Z L 2004 Phys. Rev. E 70 056406

    [6]

    Ma S H, Wu X H, Fang J P, Zheng C L 2008 Acta Phys. Sin. 57 11 (in Chinese) [马松华, 吴小红, 方建平, 郑春龙 2008 物理学报 57 11]

    [7]

    Xie B S, Du S C 2006 Phys. Plasmas 13 074504

    [8]

    Xie B S, Li H B, Hu B B 2005 Eur. Phys. Lett. 69 358

    [9]

    Xie B S, Wang N C 2002 Phys. Scr. 65 444

    [10]

    Xie B S, Yu M Y 2000 Phys. Plasmas 7 3137

    [11]

    Xie B S, He K F, Huang Z Q, 2000 Chin. Phys. Lett. 17 815

    [12]

    Xie B S, He K F, Huang Z Q 1999 Phys. Plasmas 6 3808

    [13]

    Huang G X, Velarde M G, Makrov V A 2001 Phys. Rev. A 64 013617

    [14]

    Duan W S 2004 Chin. Phys. 13 598

    [15]

    Duan W S 2004 Chaos, Solitons and Fractals 21 319

    [16]

    Mao J J, Yang J R 2007 Acta Phys. Sin. 56 5049 (in Chinese) [毛杰健, 杨建荣 2007 物理学报 56 5049]

    [17]

    Lu D C, Hong B J, Tian L X 2006 Acta Phys. Sin. 55 5617 (in Chinese) [卢殿臣, 洪宝剑, 田立新 2006 物理学报 55 5617]

    [18]

    Han J N, Li S C, Yang X X, Duan W S 2008 Eur. Phys. J. D 47 197

    [19]

    Mushtaq A, Khan S A 2007 Phys. Plasmas 14 052307

    [20]

    Xiao D L, Ma J X, Li Y F, Xia Y H, Yu M Y 2006 Phys. Plasmas 13 052308

    [21]

    Goerts C K 1998 Rev. Geophys. 27 271

    [22]

    Havnes O, Melandse F, La Hoz C, Aslaksen T K, Hartquist T 1992 Phys. Scr. 45 433

    [23]

    Benkadda S, Tsytovich V N, Verga A 1995 Comments Plasmas Phys. Cont. Fus. 16 321

    [24]

    Verheest F 1996 Space Sci. Rev. 77 267

    [25]

    Shukla P K, Silin V P, Yu My 1992 Phys. Scr. 45 508

    [26]

    Barkar A, Meclino R L, D'Angelo N 1995 Phys. Plasma 2 3563

    [27]

    Morfill G E, Thomos H 1996 J. Vac. Sci. Technol. A 14 490

    [28]

    Merlino R L, Barkan A, Thompson C, D'Angelo N 1990 Plant Space Sci. 38 1143

    [29]

    Duan W S 2001 Phys. Plasmas 8 3583

    [30]

    Hong X R, Duan W S, Song J A, Shi Y R, Lü K P 2003 Acta Phys. Sin. 52 2671 (in Chinese) [洪学仁, 段文山, 孙建安, 石玉仁, 吕克璞 2003 物理学报 52 2671]

    [31]

    Shi Y R, Zhang J, Yang H J, Duan W S 2011 Acta Phys. Sin. 60 020402 (in Chinese) [石玉仁, 张娟, 杨红娟, 段文山 2011 物理学报 60 020402]

    [32]

    Shi Y R, Zhang J, Yang H J, Duan W S, Karl E Lonngren 2011 Chin. Phys. B 20 015205

    [33]

    Das J, Bandyopadhyay A, Das K P 2007 Phys. Plasmas 14 092403

    [34]

    Singh D K, Malik H K 2007 Plasma Phys. Contr. F 49 1551

    [35]

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

    [36]

    Han J N, Yang X X, Tian D X, Duan W S 2008 Phys. Lett. A 372 4817

    [37]

    Tian B, Gao Y T 2007 Phys. Lett. A 362 283

    [38]

    Duan W S, Hong X R 2003 Acta Phys. Sin. 52 1337 (in Chinese) [段文山, 洪学仁 2003 物理学报 52 1337]

    [39]

    Ikezi H, Taylor R J, Baker D R 1970 Phys. Rev. Lett. 25 11

    [40]

    Schamel H 1973 Phys. Plasmas 9 377

Metrics
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Publishing process
  • Received Date:  09 August 2011
  • Accepted Date:  20 November 2011
  • Published Online:  05 July 2012

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