搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

变系数非线性Schrödinger方程的孤子解及其相互作用

钱存 王亮亮 张解放

引用本文:
Citation:

变系数非线性Schrödinger方程的孤子解及其相互作用

钱存, 王亮亮, 张解放

Solitons of nonlinear Schrödinger equation withvariable-coefficients and interaction

Qian Cun, Wang Liang-Liang, Zhang Jie-Fang
PDF
导出引用
  • 在光孤子通信和Bose-Einstein凝聚体动力学研究中,求解广义非线性Schrödinger方程是一个重要的研究方向.稳定的孤子模式具有潜在的应用,可为实验技术的实现提供依据.本文引进一种相似变换,将变系数非线性Schrödinger方程转化成非线性Schrödinger方程,并利用已知解深入研究变系数非线性Schrödinger方程解的单孤子解、两孤子解和连续波背景下的孤子解.同时通过选择不同的具体参数,给出它们的图像分析和相应的讨论.
    Search for exact solutions to the generalized nonlinear Schrödinger equation is one of the essential directions in studies of the nonlinear dynamics in optical soliton and Bose-Einstein condensates. Stable soliton modes are of great significance for the experimental realization and potential application. In this paper, based on the introduction of a similarity transformation, the variable-coefficient nonlinear Schrödinger equation is transformed into the nonlinear Schrödinger equation, and then the single soliton solution, two-soliton solution and soliton solution in continuous-wave background for the variable coefficient nonlinear Schrödinger equation are obtained by using the known solutions. Meanwhile, their image analysis and relative discussion are given by selecting the different parameters in detail.
    • 基金项目: 国家自然科学基金(批准号:10672147, 11072219)和浙江师范大学创新团队计划资助的课题.
    [1]

    Thacker H B 1981 Rev. Mod. Phys. 53 253

    [2]

    Bogatyrev V A, Bubnov M M, Dianov E M,Kurkov A S, Mamyshev P V, Prokhorov A M, Rumyantsev S D, Semenov V A, Semenov S L, Sysoliatin A A, Chernikov S V, Guryanov A N, Devyatykh G G, Miroshnichenko S I 1991 J. Lightwave Technol. 9 561

    [3]

    Mamyshev P V, Chers V, Dianov M 1991 IEEE J. Quantum Electron. 7 2347

    [4]

    Taijima K 1987 Opt. Lett. 12 54

    [5]

    Bordon E E, Anderson W L 1989 J. Lightwave Technol. 7 353

    [6]

    Wabnitz S 1996 Opt. Lett. 21 638

    [7]

    Kuehl H H 1988 J. Opt. Soc. Am. B 5 709

    [8]

    Smith N J, Doran N J 1996 Opt. Lett. 21 570

    [9]

    Kivshar Y S, Konotop V V 1989 Sov. J . Quantum Electron. 19 566

    [10]

    Quiroga-Teixeiro M L, Andrekson P A 1996 J. Opt. Soc. Am. B 13 687

    [11]

    Gabitov I R, Turitsyn S K 1996 Opt.Lett. 21 37

    [12]

    Zhang J F, Cheng F Y 2001 Acta Phys. Sin. 50 1648 (in Chinese)[张解放、陈芳跃 2001 物理学报 50 1648 ]

    [13]

    Lou S Y, Ruan H Y 1992 Acta Phys. Sin. 41 182 (in Chinese)[楼森岳、阮航宇 1992 物理学报 41 182 ]

    [14]

    Liu S K, Fu Z T, Liu S D, Zhao Q 2002 Acta Phys. Sin. 51 1923 (in Chinese)[刘式适、付遵涛、刘式达、赵 强 2002 物理学报 51 1923 ]

    [15]

    Xu C Z, Zhang J F 2004 Acta Phys. Sin. 53 3652(in Chinese) [徐昌智、张解放 2004 物理学报 53 3652]

    [16]

    Hao R Y, Lu L, Li Z H 2004 Opt. Commun. 79 236

    [17]

    Li B, Chen Y 2004 Chaos Soliton Fract. 21 241

    [18]

    Kruglov V I, Peacock A C, Harvery J D 2003 Phys. Rev. Lett. 90 11392

    [19]

    Zong F D, Dai C Q, Yang Q, Zhang J F 2006 Acta Phys. Sin. 55 3805 [宗丰德、戴朝卿、杨 琴、张解放 2006 物理学报 55 3805]

    [20]

    Belmonte-Beitia J, Pérez-García V M, Vekslerchik V,Konotop V V 2008 Phys. Rev. Lett. 100 164102

    [21]

    Belmonte-Beitia J,Cuevas J 2009 J. Phys. A 42 165201

    [22]

    Yan J R 1996 Chin. Sci. Bull. 41 17

    [23]

    Bélanger N, Bélanger P A 1996 Opt. Commun. 124 301

    [24]

    He J S, Ji M,Li Y S 2007 Chin. Phys. Lett. 24 8

    [25]

    Sergey A P,Govind P A 2006 Phys. Rev. Lett. 97 013901

  • [1]

    Thacker H B 1981 Rev. Mod. Phys. 53 253

    [2]

    Bogatyrev V A, Bubnov M M, Dianov E M,Kurkov A S, Mamyshev P V, Prokhorov A M, Rumyantsev S D, Semenov V A, Semenov S L, Sysoliatin A A, Chernikov S V, Guryanov A N, Devyatykh G G, Miroshnichenko S I 1991 J. Lightwave Technol. 9 561

    [3]

    Mamyshev P V, Chers V, Dianov M 1991 IEEE J. Quantum Electron. 7 2347

    [4]

    Taijima K 1987 Opt. Lett. 12 54

    [5]

    Bordon E E, Anderson W L 1989 J. Lightwave Technol. 7 353

    [6]

    Wabnitz S 1996 Opt. Lett. 21 638

    [7]

    Kuehl H H 1988 J. Opt. Soc. Am. B 5 709

    [8]

    Smith N J, Doran N J 1996 Opt. Lett. 21 570

    [9]

    Kivshar Y S, Konotop V V 1989 Sov. J . Quantum Electron. 19 566

    [10]

    Quiroga-Teixeiro M L, Andrekson P A 1996 J. Opt. Soc. Am. B 13 687

    [11]

    Gabitov I R, Turitsyn S K 1996 Opt.Lett. 21 37

    [12]

    Zhang J F, Cheng F Y 2001 Acta Phys. Sin. 50 1648 (in Chinese)[张解放、陈芳跃 2001 物理学报 50 1648 ]

    [13]

    Lou S Y, Ruan H Y 1992 Acta Phys. Sin. 41 182 (in Chinese)[楼森岳、阮航宇 1992 物理学报 41 182 ]

    [14]

    Liu S K, Fu Z T, Liu S D, Zhao Q 2002 Acta Phys. Sin. 51 1923 (in Chinese)[刘式适、付遵涛、刘式达、赵 强 2002 物理学报 51 1923 ]

    [15]

    Xu C Z, Zhang J F 2004 Acta Phys. Sin. 53 3652(in Chinese) [徐昌智、张解放 2004 物理学报 53 3652]

    [16]

    Hao R Y, Lu L, Li Z H 2004 Opt. Commun. 79 236

    [17]

    Li B, Chen Y 2004 Chaos Soliton Fract. 21 241

    [18]

    Kruglov V I, Peacock A C, Harvery J D 2003 Phys. Rev. Lett. 90 11392

    [19]

    Zong F D, Dai C Q, Yang Q, Zhang J F 2006 Acta Phys. Sin. 55 3805 [宗丰德、戴朝卿、杨 琴、张解放 2006 物理学报 55 3805]

    [20]

    Belmonte-Beitia J, Pérez-García V M, Vekslerchik V,Konotop V V 2008 Phys. Rev. Lett. 100 164102

    [21]

    Belmonte-Beitia J,Cuevas J 2009 J. Phys. A 42 165201

    [22]

    Yan J R 1996 Chin. Sci. Bull. 41 17

    [23]

    Bélanger N, Bélanger P A 1996 Opt. Commun. 124 301

    [24]

    He J S, Ji M,Li Y S 2007 Chin. Phys. Lett. 24 8

    [25]

    Sergey A P,Govind P A 2006 Phys. Rev. Lett. 97 013901

计量
  • 文章访问数:  6728
  • PDF下载量:  1902
  • 被引次数: 0
出版历程
  • 收稿日期:  2010-03-29
  • 修回日期:  2010-09-14
  • 刊出日期:  2011-03-05

变系数非线性Schrödinger方程的孤子解及其相互作用

  • 1. 浙江师范大学非线性物理研究所,金华 321004
    基金项目: 国家自然科学基金(批准号:10672147, 11072219)和浙江师范大学创新团队计划资助的课题.

摘要: 在光孤子通信和Bose-Einstein凝聚体动力学研究中,求解广义非线性Schrödinger方程是一个重要的研究方向.稳定的孤子模式具有潜在的应用,可为实验技术的实现提供依据.本文引进一种相似变换,将变系数非线性Schrödinger方程转化成非线性Schrödinger方程,并利用已知解深入研究变系数非线性Schrödinger方程解的单孤子解、两孤子解和连续波背景下的孤子解.同时通过选择不同的具体参数,给出它们的图像分析和相应的讨论.

English Abstract

参考文献 (25)

目录

    /

    返回文章
    返回