 Born approximation for a one-dimensional reflection coefficient

ID: born-approximation-for-a-one-dimensional-reflection-coefficient

For a weak potential

u = ϵ q

, the first Born approximation in the KdV Schrödinger convention is

R (k) = \frac{ϵ}{2 ik} \int_{R} e^{- 2 ik x} q (x) d x + O (ϵ^{2}) .

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