论文标题
非线性Helmholtz方程的逆介质散射
Inverse medium scattering for a nonlinear Helmholtz equation
论文作者
论文摘要
我们讨论了一个非线性Helmholtz方程的时间谐波反向散射问题，其紧凑型不均匀散射对象是由无限制的自由空间中非线性折射率描述的。假设对非线性远场操作员的知识，将HERGLOTZ的入射波映射到非线性散射问题的相应解的远场模式，我们表明折射的非线性折射索引是唯一确定的。我们还概括了两种重建方法，一种分解方法和一种单调性方法，以恢复对此类非线性散射对象的支持。数值结果说明了我们的理论发现。
We discuss a time-harmonic inverse scattering problem for a nonlinear Helmholtz equation with compactly supported inhomogeneous scattering objects that are described by a nonlinear refractive index in unbounded free space. Assuming the knowledge of a nonlinear far field operator, which maps Herglotz incident waves to the far field patterns of corresponding solutions of the nonlinear scattering problem, we show that the nonlinear index of refraction is uniquely determined. We also generalize two reconstruction methods, a factorization method and a monotonicity method, to recover the support of such nonlinear scattering objects. Numerical results illustrate our theoretical findings.
