论文标题
非线性schrodinger方程的形状修复降低级模型
Shape-morphing reduced-order models for nonlinear Schrodinger equations
论文作者
论文摘要
我们考虑通过一类非线性Schrodinger（NLS）方程描述的非线性分散波的降低级建模。我们比较了两种非线性降阶建模方法：（i）依赖于NLS的变异公式的简化拉格朗日方法，以及（ii）最近开发的还原级非线性溶液（RONS）的方法。首先，我们证明了令人惊讶的结果，尽管这两种方法似乎完全不同，但它们可以从单个复杂值值的主方程的真实和虚构部分获得。此外，对于固定框架中的NLS方程，我们表明降低的Lagrangian方法无法预测波的正确组速度，而Rons则预测了正确的组速度。最后，对于修改的NLS方程，减少的Lagrangian方法是不可应用的，RONS还原模型准确地近似于真实的解决方案。
We consider reduced-order modeling of nonlinear dispersive waves described by a class of nonlinear Schrodinger (NLS) equations. We compare two nonlinear reduced-order modeling methods: (i) The reduced Lagrangian approach which relies on the variational formulation of NLS and (ii) The recently developed method of reduced-order nonlinear solutions (RONS). First, we prove the surprising result that, although the two methods are seemingly quite different, they can be obtained from the real and imaginary parts of a single complex-valued master equation. Furthermore, for the NLS equation in a stationary frame, we show that the reduced Lagrangian method fails to predict the correct group velocity of the waves whereas RONS predicts the correct group velocity. Finally, for the modified NLS equation, where the reduced Lagrangian approach is inapplicable, the RONS reduced-order model accurately approximates the true solutions.
