Inverse spectral theory for the AKNS system with separated boundary conditions

Abstract

Results in inverse spectral theory are given for the AKNS systems with separated self-adjoint boundary conditions. More precisely we construct a coordinate system well adapted to the isospectral sets. The isospectral sets are analytic, unbounded submanifolds. We give explicit formulae for the solutions to some isospectral flows. Finally we characterize all possible spectra associated with separated self-adjoint boundary conditions.