We investigate the propagation of solitons in homogeneous nonlocal nonlinear media and in media with gradual nonlinear nonlocality. We calculate the width and the maximum amplitude of solitons during propagation and demonstrate that solitons will propagate asymmetrically in the medium with gradual nonlinear nonlocality. Moreover, the propagation of solitons in the nonlinear medium with gradual nonlocality is independent of the forms of monotonically gradual nonlocalities. Finally, we investigate the ratio of width magnification quantitatively and demonstrate that the soliton with a particular input power maintains its width in one direction and suffers strong expansion in another direction.

中文翻译：

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渐进非局部非线性介质中孤子的不对称传播

我们研究了孤子在齐次非局部非线性介质和渐进非线性非局部介质中的传播。我们计算了孤子在传播过程中的宽度和最大振幅，并证明了孤子将在具有逐步非线性非局部性的介质中不对称地传播。此外，孤子在具有渐进非局部性的非线性介质中的传播与单调渐进非局部性的形式无关。最后，我们定量研究了宽度放大率，并证明了具有特定输入功率的孤子在一个方向上保持其宽度而在另一个方向上遭受了强烈的膨胀。