Nonelliptic Schrödinger equations
Nonelliptic Schrödinger equations
复制标题
非椭圆薛定谔方程
DOI：
10.1007/bf02429863
复制
发表时间：
1993
影响因子：
3
通讯作者：
J. Saut
中科院分区：
文献类型：
--
作者：
J. Ghidaglia;J. Saut
非椭圆薛定谔方程定义为多维非线性色散波方程，其空间变量中的线性部分不是椭圆方程。这些方程在物理学和流体力学的几种情况下以自然的方式出现。该文致力于研究两个问题.首先，简要回顾了作者所知的主要非椭圆薛定谔方程，重点讨论了水波。第二，针对所选的例子，发展了柯西问题的理论。该方法基于与问题的色散关系密切相关的线性估计。
SummaryNonelliptic Schrödinger equations are defined as multidimensional nonlinear dispersive wave equations whose linear part in the space variables is not an elliptic equation. These equations arise in a natural fashion in several contexts in physics and fluid mechanics. The aim of this paper is twofold. First, a brief survey is made of the main nonelliptic Schrödinger equations known by the authors, with emphasis on water waves. Second, a theory is developed for the Cauchy problem for selected examples. The method is based on linear estimates which are strongly related to the dispersion relation of the problem.