论文标题
通过整数功率类型非线性，提高一阶线性化逆Schrödinger潜在问题的稳定性
Increasing stability of the first order linearized inverse Schrödinger potential problem with integer power type nonlinearities
论文作者
论文摘要
我们研究了大型波数在大型波数中的整数功率类型非线性的反向Schrödinger潜在问题的稳定性提高。通过考虑一阶线性化系统相对于未知电位函数，提出了一阶线性化的组合公式，该公式为LIPSCHITZ类型稳定性提供了恢复在低频模式下未知电位函数的傅立叶系数。这些稳定性结果突出了非线性在解决此反向潜在问题方面的优势，通过明确量化对波数和非线性指数的依赖性。还提供了通用功率类型非线性的重建算法。几个数值示例阐明了我们提出的算法的效率。
We investigate the increasing stability of the inverse Schrödinger potential problem with integer power type nonlinearities at a large wavenumber. By considering the first order linearized system with respect to the unknown potential function, a combination formula of the first order linearization is proposed, which provides a Lipschitz type stability for the recovery of the Fourier coefficients of the unknown potential function in low frequency mode. These stability results highlight the advantage of nonlinearity in solving this inverse potential problem by explicitly quantifying the dependence to the wavenumber and the nonlinearities index. A reconstruction algorithm for general power type nonlinearities is also provided. Several numerical examples illuminate the efficiency of our proposed algorithm.
