The hybrid variational method can be used to simplify multidimensional numerical simulations. We examine the applicability of this method to study the nonlinear propagation of a single beam and the interference of two spatial soliton beams in a graded-index optical waveguide governed by a two-dimensional nonlinear Schrodinger equation. We classified three distinct regimes of the dynamics that emerge during single Gaussian beam propagation, corresponding to beam decay, breather formation, and self-focusing. When two spatial soliton beams were set up to interfere in the waveguide, we identified the boundary where the nonlinear interaction during the interference led to excitation or self-focusing. These quite involved dynamics were used to test the predictive power of our variational models by comparing them with direct numerical simulations, obtaining good agreement.

中文翻译：

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梯度折射率非线性波导中光束传播和相互作用的混合变分法


混合变分方法可用于简化多维数值模拟。我们检验了该方法在二维非线性薛定谔方程控制的渐变折射率光波导中研究单光束的非线性传播和两个空间孤子光束的干涉的适用性。我们对单高斯光束传播过程中出现的三种不同的动力学状态进行了分类，分别对应于光束衰减、呼吸形成和自聚焦。当设置两个空间孤子束在波导中进行干涉时，我们确定了干涉过程中非线性相互作用导致激发或自聚焦的边界。这些相当复杂的动力学被用来测试我们的变分模型的预测能力，通过将它们与直接数值模拟进行比较，获得良好的一致性。