论文标题
非线性schrödinger近似的有效性，具有多个导数的准色散系统
Validity of the nonlinear Schrödinger approximation for quasilinear dispersive systems with more than one derivative
论文作者
论文摘要
对于非线性分散系统，非线性schrödinger（NLS）方程通常可以作为形式近似方程得出，描述了慢的空间和时间调制，用于空间和时间上振荡的基础载体波的封底。在这里，我们证明了一类准线性分散系统的NLS近似值，其中还包括用于水波问题的玩具模型。这是第一次针对系统进行，允许准线性二次术语有效损失多个导数。在有效损失的情况下，我们意味着在对对角线部分进行对角线化后仍然存在损失，以使该对角线化中的所有线性算子具有相同的规律性特性。
For nonlinear dispersive systems, the nonlinear Schrödinger (NLS) equation can usually be derived as a formal approximation equation describing slow spatial and temporal modulations of the envelope of a spatially and temporally oscillating underlying carrier wave. Here, we justify the NLS approximation for a whole class of quasilinear dispersive systems, which also includes toy models for the waterwave problem. This is the first time that this is done for systems, where a quasilinear quadratic term is allowed to effectively lose more than one derivative. With effective loss we here mean the loss still present after making a diagonalization of the linear part of the system such that all linear operators in this diagonalization have the same regularity properties.
