论文标题
出生和反向出生的系列，用于散射Kerr非线性的问题
Born and inverse Born series for scattering problems with Kerr nonlinearities
论文作者
论文摘要
我们考虑了具有Kerr类型的立方非线性的标量波的出生和反面系列。我们为诞生的系列中的运营商找到了一个递归公式，并证明了它们的界限。该结果提供了保证诞生序列收敛的条件，随后产生的条件可以保证反向出生序列的收敛。我们还使用固定点理论为出生序列的收敛提供替代的明确条件。我们通过数值实验说明了结果。
We consider the Born and inverse Born series for scalar waves with a cubic nonlinearity of Kerr type. We find a recursive formula for the operators in the Born series and prove their boundedness. This result gives conditions which guarantee convergence of the Born series, and subsequently yields conditions which guarantee convergence of the inverse Born series. We also use fixed point theory to give alternate explicit conditions for convergence of the Born series. We illustrate our results with numerical experiments.
