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.
Received: 23 October 2006
Revised: 13 December 2006
Accepted manuscript online:
Fund: 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).
Cite this article:
Ouyang Shi-Gen(欧阳世根), Guo Qi(郭旗), Lan Sheng(兰胜), and Wu Li-Jun(吴立军) The solutions of the strongly nonlocal spatial solitons with several types of nonlocal response functions 2007 Chinese Physics 16 2325
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