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中文摘要：
在非局域非线性克尔介质中,通过对介质实对称响应函数的泰勒展开,简化了非局域非线性薛定谔方程所对应的Lagrange密度,进而利用变分法对光束的传输问题进行了分析.求出试探解各个参量的演化方程并得到了自聚焦介质中的厄米高斯型光束的精确解析解,当输入功率达到临界功率时,即形成高阶空间光孤子（厄米高斯孤子）,其最低阶（基模光孤子）就是高斯孤子.通过数值模拟发现解析解与数值解符合得很好.
英文摘要：
The reduced Lagrange density of nonlocal nonlinear Schr~dinger equation （NNLSE） is obtained by expanding the real symmetric response function in Taylor＇s series in strongly nonlocal Kerr media. The problem of higher-order beam propagation can be analyzed by a variational approach, the equations are obtained for the evolution during propagation of the parameters of the trial solution and exact analytical Hermite-Gaussian（HG） solutions are found. HG solitons are formed when the input power is equal to the critical power. We demonstrated that the analytical HG solutions are in good agreement with the numerical simulations in the case of strong nonlocality.
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