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具有色散系数的(2+1)维非线性Schrdinger方程的有理解和空间孤子

马正义 马松华 杨毅

引用本文:
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具有色散系数的(2+1)维非线性Schrdinger方程的有理解和空间孤子

马正义, 马松华, 杨毅

Rational solutions and spatial solitons for the (2+1)-dimensional nonlinear Schrdinger equation with distributed coefficients

Ma Zheng-Yi, Ma Song-Hua, Yang Yi
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  • 非线性Schrdinger方程是物理学中具有广泛应用的非线性模型之一. 本文采用相似变换, 将具有色散系数的(2+1)维非线性Schrdinger方程简化成熟知的Schrdinger方程, 进而得到原方程的有理解和一些空间孤子.
    The nonlinear Schrdinger equation is one of the most important nonlinear models with widely applications in physics. Based on a similarity transformation, the (2+1)-dimensional nonlinear Schrdinger equation with distributed coefficients is transformed into a traceable nonlinear Schrdinger equation, and then two types of rational solutions and several spatial solitons are derived.
    • 基金项目: 应用非线性科学与技术浙江省重中之重学科开放基金和浙江省自然科学基金(批准号:Y606049, Y6100257)资助的课题.
    • Funds: Project supported by the Applied Nonlinear Science and Technology from the most important among all the top priority disciplines of Zhejiang Province and the Natural Science Foundation of Zhejiang Province, China (Grant Nos. Y606049, Y6100257).
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    [2]

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    [5]

    Zhang J F, Dai C Q, Yang Q, Zhu J M 2005 Opt. Commun. 252 408

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    [10]

    Chen S, Yi L, Guo D S, Lu P 2005 Phys. Rev. E 72 016622

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    Kruglov V I, Peacock A C, Harvey J D 2005 Phys. Rev. E 71 056619

    [12]

    Zhong W P, Xie R H, Belić M, Petrović N, Chen G, Yi L 2008 Phys. Rev. A 78 023821

    [13]

    Dai C Q, Zhang J F 2010 Opt. Lett. 35 2651

    [14]

    Dai C Q, Zhu S Q, Zhang J F 2010 Opt. Commun. 283 3784

    [15]

    Kruglov V I, Peacock A C, Harvey J D 2003 Phys. Rev. Lett. 90 113902

    [16]

    Chen S H, Dudley J M 2009 Phys. Rev. Lett. 102 233903

    [17]

    Qian C, Wang L L, Zhang J F 2011 Acta Phys. Sin. 60 064214 (in Chinese) [钱存, 王亮亮, 张解放 2011 物理学报 60 064214]

    [18]

    Yan Z Y, Konotop V V, Akhmediev 2010 Phys. Rev. E 82 036610

    [19]

    Akhmediev N, Soto-Crespo J M, Ankiewicz A 2009 Phys. Lett. A 373 2137

    [20]

    Akhmediev N, Ankiewicz A, Soto-Crespo J M 2009 Phys. Rev. E 80 026601

    [21]

    Yan Z Y 2010 Commun. Theor. Phys. (Beijing, China) 54 947

    [22]

    Yan Z Y 2010 Phys. Lett. A 374 672

  • [1]

    Kivshar Y, Agrawal G P 2003 Optical Solitons: From Fibers to Photonic Crystals (New York: Academic Press)

    [2]

    Dodd R K, Eilbeck J C, Gibbon J D, Morris H C 1982 Solitons and nonlinear wave equations (New York: Academic Press)

    [3]

    Pitaevskii L P, Stringari S 2003 Bose-Einstein Condensation (Oxford: Oxford University Press)

    [4]

    Scott A 1999 Nonlinear Science: Emergence and Dynamics of Coherent Structures (Vol. 1) (Oxford: Oxford University Press)

    [5]

    Zhang J F, Dai C Q, Yang Q, Zhu J M 2005 Opt. Commun. 252 408

    [6]

    Zhao L H, Dai C Q 2010 Eur. Phys. J. D 58 327

    [7]

    Dai C Q, Wang Y Y, Zhang J F 2010 Opt. Express 35 17548

    [8]

    Dai C Q, Wang X G, Zhang J F 2011 Ann. Phys. 326 645

    [9]

    Zong F D, Dai C Q, Yang Q, Zhang J F 2006 Acta Phys. Sin. 55 3805 (in Chinese) [宗丰德, 戴朝卿, 杨琴, 张解放 2006 物理学报 55 3805]

    [10]

    Chen S, Yi L, Guo D S, Lu P 2005 Phys. Rev. E 72 016622

    [11]

    Kruglov V I, Peacock A C, Harvey J D 2005 Phys. Rev. E 71 056619

    [12]

    Zhong W P, Xie R H, Belić M, Petrović N, Chen G, Yi L 2008 Phys. Rev. A 78 023821

    [13]

    Dai C Q, Zhang J F 2010 Opt. Lett. 35 2651

    [14]

    Dai C Q, Zhu S Q, Zhang J F 2010 Opt. Commun. 283 3784

    [15]

    Kruglov V I, Peacock A C, Harvey J D 2003 Phys. Rev. Lett. 90 113902

    [16]

    Chen S H, Dudley J M 2009 Phys. Rev. Lett. 102 233903

    [17]

    Qian C, Wang L L, Zhang J F 2011 Acta Phys. Sin. 60 064214 (in Chinese) [钱存, 王亮亮, 张解放 2011 物理学报 60 064214]

    [18]

    Yan Z Y, Konotop V V, Akhmediev 2010 Phys. Rev. E 82 036610

    [19]

    Akhmediev N, Soto-Crespo J M, Ankiewicz A 2009 Phys. Lett. A 373 2137

    [20]

    Akhmediev N, Ankiewicz A, Soto-Crespo J M 2009 Phys. Rev. E 80 026601

    [21]

    Yan Z Y 2010 Commun. Theor. Phys. (Beijing, China) 54 947

    [22]

    Yan Z Y 2010 Phys. Lett. A 374 672

计量
  • 文章访问数:  5935
  • PDF下载量:  514
  • 被引次数: 0
出版历程
  • 收稿日期:  2012-02-24
  • 修回日期:  2012-03-31

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