中国物理B ›› 2007, Vol. 16 ›› Issue (8): 2325-2330.doi: 10.1088/1009-1963/16/8/028

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The solutions of the strongly nonlocal spatial solitons with several types of nonlocal response functions

欧阳世根, 郭旗, 兰胜, 吴立军   

  1. Laboratory of Photonic Information Technology, South China Normal University, Guangzhou 510631, China
  • 收稿日期:2006-10-23 修回日期:2006-12-13 出版日期:2007-08-20 发布日期:2007-08-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10474023 and 10674050) and Specialized Research Fund for the Doctoral Program of Higher Education (Grant No 20060574006).

The solutions of the strongly nonlocal spatial solitons with several types of nonlocal response functions

Ouyang Shi-Gen(欧阳世根),Guo Qi(郭旗)†, Lan Sheng(兰胜), and Wu Li-Jun(吴立军)   

  1. Laboratory of Photonic Information Technology, South China Normal University, Guangzhou 510631, China
  • Received:2006-10-23 Revised:2006-12-13 Online:2007-08-20 Published:2007-08-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10474023 and 10674050) and Specialized Research Fund for the Doctoral Program of Higher Education (Grant No 20060574006).

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摘要： The fundamental and second order strongly nonlocal solitons of the nonlocal nonlinear Schr\"{o}dinger equation for several types of nonlocal responses are calculated by Ritz's variational method. For a specific type of nonlocal response, the solutions of the strongly nonlocal solitons with the same beam width but different degrees of nonlocality are identical except for an amplitude factor. For a nonlocal case where the nonlocal response function decays in direct proportion to the $m$th power of the distance near the source point, the power and the phase constant of the strongly nonlocal soliton are in inverse proportion to the $(m+2)$th power of its beam width.

Abstract: The fundamental and second order strongly nonlocal solitons of the nonlocal nonlinear Schrödinger equation for several types of nonlocal responses are calculated by Ritz's variational method. For a specific type of nonlocal response, the solutions of the strongly nonlocal solitons with the same beam width but different degrees of nonlocality are identical except for an amplitude factor. For a nonlocal case where the nonlocal response function decays in direct proportion to the $m$th power of the distance near the source point, the power and the phase constant of the strongly nonlocal soliton are in inverse proportion to the $(m+2)$th power of its beam width.

Key words: nonlocal nonlinear Schrödinger equation, strong nonlocality, spatial optical soliton

中图分类号:  (Solitons)

  • 05.45.Yv
03.65.Ge (Solutions of wave equations: bound states)