Evans Function for the AKNS Problem with Algebraic Solitons

We study renormalization of the Evans function for the AKNS spectral problem on a real line with algebraically decaying potentials. We show that the Evans function may have pole singularities at embedded eigenvalues of the essential spectrum, which are related to algebraically decaying eigenfunctions. Stability of algebraic solitons in the initial-value problem for the modified KdV equation is studied with the renormalized Evans function.