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中文摘要：
利用变分法研究了（2＋1）维圆对称双曲正割光束在弱非局域非线性介质中的传输,得到了描述光束束宽、相位、波前曲率、振幅演化的一组微分方程,并得到了光束做孤子传输的临界功率;通过稳定性分析给出了弱非局域情形非局域效应对光束传输的稳定作用的定量描述,从而自洽地阐述了由不稳定的（2＋1）维克尔孤子到稳定的（2＋1）维弱非局域孤子的过渡情形.数值模拟的结果验证了变分计算结果的正确性,并说明圆对称的双曲正割函数是（2＋1）维弱非局域空间孤子的很好的近似.
英文摘要：
The propagation of （2＋1）D paraxial symmetrical hyperbolic secant beams in weakly nonlocal nonlinear media is studied by variational approach. A series of differential equations which describe the evolutions of the width, the phase, the phase front curvature, and the amplitude of the beam are obtained. The critical power for a beam propagating as a spatial optical soliton in weakly nonlocal nonlinear media is also obtained. A quantitative depiction of the steadying effect of nonlocality on the propagation of a beam is obtained through the steadiness analyse, which provides a self-consistent explanation of the transition from unsteady local kerr solitons to steady weakly nonlocal solitons. The results of numerical method agree with that of variational calculations, implying that hyperbolic secant function is a good approximation to a （2＋1）D weakly nonlocal spatial optical soliton.
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