Solution
= Solution
The <discrete scattering data>[scattering data for the Schrodinger operator] consist of the reflection coefficient $R(k,t)$ on the continuous spectrum, the negative discrete eigenvalues $-\kappa_n^2$, and their norming constants $c_n$. Isospectrality gives
$$
\kappa_n(t)=\kappa_n(0).
$$
Comparing the asymptotic plane waves in $\psi_t=A\psi$ gives
$$
\boxed{R(k,t)=R(k,0)e^{8ik^3t},
\qquad
c_n(t)=c_n(0)e^{4\kappa_n^3t}.}
$$