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KdV Schrodinger spectral problem

KdV scattering data

{c}

For a weak potential $u=\epsilon q$, the first <Born approximation> in the KdV Schrödinger convention is
$$
R(k)=\frac{\epsilon}{2ik}\int_{\mathbb R}e^{-2ikx}q(x)\,dx+O(\epsilon^2).
$$

Born approximation for a one-dimensional reflection coefficient

Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 2 / 33C / iii / Solution

Born approximation for a one-dimensional reflection coefficient

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Born approximation for a one-dimensional reflection coefficient

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