长程势中多维Newton方程的高能逆散射
Inverse scattering at high energies for the multidimensional Newton equation in a long range potential
摘要：
我们定义散射数据的牛顿方程在潜在的$V\in C^2(\R^n,\R)$，$n\ge2$，在无穷大衰减像$r^{-α}$一些$α\in (0,1]$。我们提供的散射解决方案和散射数据的估计，我们证明，特别是，在高能量的散射数据唯一确定的短期部分的潜在知识的长期尾巴的潜力。在散射数据的固定能量的玻恩近似也被认为是。然后，我们改变散射数据的定义，研究在其他渐近制度的逆散射。这些结果是通过发展[Novikov，1999]的逆散射方法获得的。
英文摘要：
We define scattering data for the Newton equation in a potential $V\in C^2(\R^n,\R)$, $n\ge2$, that decays at infinity like $r^{-α}$ for some $α\in (0,1]$. We provide estimates on the scattering solutions and scattering data and we prove, in particular, that the scattering data at high energies uniquely determine the short range part of the potential up to the knowledge of the long range tail of the potential. The Born approximation at fixed energy of the scattering data is also considered. We then change the definition of the scattering data to study inverse scattering in other asymptotic regimes. These results were obtained by developing the inverse scattering approach of [Novikov, 1999].
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