Generalized matrix exponential solutions to the AKNS equation are obtained by the inverse scattering transformation (IST). The\nresulting solutions involve six matrices, which satisfy the coupled Sylvester equations. Several kinds of explicit solutions including\nsoliton, complexiton, and Matveev solutions are deduced from the generalized matrix exponential solutions by choosing different\nkinds of the six involved matrices. Generalized matrix exponential solutions to a general integrable equation of the AKNS hierarchy\nare also derived. It is shown that the general equation and its matrix exponential solutions share the same linear structure.
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