论文标题
1D广义Bi-Schrödinger流的唯一性
Uniqueness of 1D Generalized Bi-Schrödinger Flow
论文作者
论文摘要
我们确定了从一维平坦的圆环到紧凑的局部赫尔米尼亚对称空间的平滑普遍的Bi-Schrödinger流的独特性。由从流量引起的下拉束的部分满足的管理方程是四阶非线性分散偏微分方程，并损失了衍生物。为了显示独特性，我们采用了一种外部方法，通过将等距嵌入到环境欧几里得空间中比较两种溶液。我们引入了一种能量，以修改经典的$ h^2 $ - 能量，以差为两种解决方案的差异，详细的估计值使我们能够消除衍生物损失的困难。特别是，我们通过利用局部遗产对称空间的几何结构来证明如何决定修饰的形式。
We establish the uniqueness of a smooth generalized bi-Schrödinger flow from the one-dimensional flat torus into a compact locally Hermitian symmetric space. The governing equation, which is satisfied by sections of the pull-back bundle induced from the flow, is a fourth-order nonlinear dispersive partial differential equation with loss of derivatives. To show the uniqueness, we adopt an extrinsic approach to compare two solutions via an isometric embedding into an ambient Euclidean space. We introduce an energy modifying the classical $H^2$-energy for the difference of two solutions, the detailed estimate of which enables us to eliminate the difficulty of the loss of derivatives. In particular, we demonstrate how to decide the form of the modification by exploiting the geometric structure of the locally Hermitian symmetric space.
