具 Kerr 非线性散射问题的 Born 级数与逆 Born 级数
数值分析
2022-11-15 v1 数值分析
偏微分方程分析
摘要
我们考虑具 Kerr 型三次非线性的标量波的 Born 级数与逆 Born 级数。我们给出了 Born 级数中算子的递推公式并证明了其有界性。该结果给出了保证 Born 级数收敛的条件，并随之给出了保证逆 Born 级数收敛的条件。我们还利用不动点理论给出了 Born 级数收敛的另一种显式条件。我们通过数值实验说明了我们的结果。
引用
@article{arxiv.2211.07352,
title = {Born and inverse Born series for scattering problems with Kerr nonlinearities},
author = {Nicholas Defilippis and Shari Moskow and John C. Schotland},
journal= {arXiv preprint arXiv:2211.07352},
year = {2022}
}