论文标题
固定角度散射问题与一阶扰动
The fixed angle scattering problem with a first order perturbation
论文作者
论文摘要
我们研究了与有限多个平面波相对应的散射测量值确定磁场和电势的反散射问题。主要结果表明，系数由$ 2N $的测量量唯一确定为天然量规。我们还表明，对于没有规格不变性的相关方程，可以恢复整个一阶术语，并且如果系数具有某些对称性，则可以减少测量数量。这项工作将Rakesh和M. Salo的固定角度散射结果扩展到一阶扰动的汉密尔顿人，它基于波方程方法和Carleman估计。
We study the inverse scattering problem of determining a magnetic field and electric potential from scattering measurements corresponding to finitely many plane waves. The main result shows that the coefficients are uniquely determined by $2n$ measurements up to a natural gauge. We also show that one can recover the full first order term for a related equation having no gauge invariance, and that it is possible to reduce the number of measurements if the coefficients have certain symmetries. This work extends the fixed angle scattering results of Rakesh and M. Salo to Hamiltonians with first order perturbations, and it is based on wave equation methods and Carleman estimates.
