论文标题
非线性schrödinger方程的小能量和精制轮廓的坐标
Coordinates at small energy and refined profiles for the Nonlinear Schrödinger Equation
论文作者
论文摘要
在本文中，我们为我们在\ cite {cm15apde}中给出的非线性schrödinger方程（NLS）的小能量解决方案（NLS）提供了新的和简化的定理证明。我们考虑使用带有几个特征值的Schrödinger操作员的NLS，具有相应的站立波的家族，我们表明，任何小能量溶液都会收敛于时间周期溶液的轨道以及散射项。新颖的想法是考虑“精制概况”，即及时几乎解决NLS并编码解决方案的离散模式的“精制轮廓”。通过基本均值获得的精制轮廓为我们提供了一个最佳的坐标系，避免了\ cite {cm15apde}中的正常形式参数，这也使我们更好地理解了Fermi Golden规则。
In this paper we give a new and simplified proof of the theorem on selection of standing waves for small energy solutions of the nonlinear Schrödinger equations (NLS) that we gave in \cite{CM15APDE}. We consider a NLS with a Schrödinger operator with several eigenvalues, with corresponding families of small standing waves, and we show that any small energy solution converges to the orbit of a time periodic solution plus a scattering term. The novel idea is to consider the "refined profile", a quasi--periodic function in time which almost solves the NLS and encodes the discrete modes of a solution. The refined profile, obtained by elementary means, gives us directly an optimal coordinate system, avoiding the normal form arguments in \cite{CM15APDE}, giving us also a better understanding of the Fermi Golden Rule.
