散焦非线性薛定谔方程中一个和两个暗孤子条纹的约化动力学：变分法
Reduced dynamics for one and two dark soliton stripes in the defocusing nonlinear Schrödinger equation: a variational approach
摘要：
研究了二维散焦非线性薛定谔方程中暗孤子条纹的动力学和两两相互作用。通过采用变分方法，我们减少了暗孤子条纹的动力学的一组耦合的一维“丝”的条纹的位置和速度的运动方程。该方法产生良好的定性协议的数值结果方面的横向不稳定性的条纹。我们提出了一个现象学的修正，也显着提高了定量协议的方法与计算。随后，该方法被扩展到一对对称的暗孤子条纹，其中包括丝之间的相互作用。减少的运动方程与最近提出的绝热不变的方法和相应的调查结果进行比较，并发现提供了一个更充分的代表性的原始完整的动态范围广泛的情况下，包括长波长和短波长的扰动，以及它们的组合。
英文摘要：
We study the dynamics and pairwise interactions of dark soliton stripes in the two-dimensional defocusing nonlinear Schrödinger equation. By employing a variational approach we reduce the dynamics for dark soliton stripes to a set of coupled one-dimensional "filament" equations of motion for the position and velocity of the stripe. The method yields good qualitative agreement with the numerical results as regards the transverse instability of the stripes. We propose a phenomenological amendment that also significantly improves the quantitative agreement of the method with the computations. Subsequently, the method is extended for a pair of symmetric dark soliton stripes that include the mutual interactions between the filaments. The reduced equations of motion are compared with a recently proposed adiabatic invariant method and its corresponding findings and are found to provide a more adequate representation of the original full dynamics for a wide range of cases encompassing perturbations with long and short wavelengths, and combinations thereof.
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