A characterization of all elliptic algebro-geometric solutions of the AKNS hierarchy

Here ~9(x):p(x; wl,w3) denotes the elliptic Weierstrass function with fundamental periods 2wl and 2w3 (Im(w3/Wl)#0). In the special case where Wl is real and w3 is purely imaginary, the potential q(x) in (1.1) is real-valued and Ince's striking result [51], in modern spectral-theoretic terminology, yields that the spectrum of the unique self-adjoint operator associated with the differential expression L2=d2/dx 2 +q(x) in L2(R) exhibits finitely many bands (and gaps, respectively), that is,