For meromorphic potentials integrable at infinity, Zakharov-Shabat systems are solvable by quadrature if and only if the potentials are reflectionless, subject to extra analyticity and spectral-zero assumptions.
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Solvability of the Zakharov-Shabat systems with meromorphic potentials by quadrature
For meromorphic potentials integrable at infinity, Zakharov-Shabat systems are solvable by quadrature if and only if the potentials are reflectionless, subject to extra analyticity and spectral-zero assumptions.