J4 ›› 2009, Vol. 26 ›› Issue (4): 465-472.

• 非线性光学 • 上一篇    下一篇

广义非局域非线性薛定谔模型的自相似解

张少武1 易林2   

  1. 1 湖北师范学院物理系, 黄石 435002; 
    2 华中科技大学物理系, 武汉 430074
  • 收稿日期:2008-09-04 修回日期:2008-11-07 出版日期:2009-07-28 发布日期:2009-06-29
  • 通讯作者: 张少武 ( 1964- ), 男, 博士, 主要从事量子光学及非线性光学研究. E-mail:zsw2622@vip.163.com

Exact self-similar solution to a generalized nonlocal nonlinear Schrödinger model

ZHANG Shao-Wu1 , Yi-Lin2   

  1. 1Department of Physics, Hubei Normal University, Huangshi 435002; 
    2 Department of Physics, Huazhong University of Science and Technology, Wuhan 430074
  • Received:2008-09-04 Revised:2008-11-07 Published:2009-07-28 Online:2009-06-29

摘要:

在获得一个含变化3-5阶非线性、弱非局域性、增益及非线性增益的广义薛定谔方程的自相似解的基础上,采用数值方法研究了解的稳定性. 结果表明,在同时具有或没有非局域性和5阶非线性的介质中可以形成与传播自相似波; 而且当相位参数远离 时,非局域度和累积衍射将极大影响自相似波的稳定性.

关键词: 非线性光学, 自相似解, 弱非局域非线性薛定谔方程, 非线性增益

Abstract:

Exact self-similar solution of a generalized nonlinear Schrödinger equation with varying cubic-quintic nonlinearity, weakly nonlocality, gain and nonlinear gain was obtained. The stability of the solution was studied numerically. The results show that the self-similar solitary wave can exist and propagate in the media with or without both nonlocality and quintic nonlinearity, and that the stability of the self-similar solitary wave is drastically influenced by the degree of nonlocality and the cumulative diffraction under the condition that the phase parameter is far from .

Key words: nonlinear optics, self-similar solution, weakly nonlocal nonlinear Schrödinger model, nonlinear gain

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