L. Amour et Jc. Guillot, ISOSPECTRAL SETS FOR AKNS SYSTEMS ON THE UNIT INTERVAL WITH GENERALIZED PERIODIC BOUNDARY-CONDITIONS, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 320(6), 1995, pp. 675-678
We analyze the isospectral sets of potentials associated with generali
zed periodic boundary conditions B in SL(2, R), for the 2 x 2 AKNS sys
tems on the unit interval. When B is orthogonal, we recover the usual
periodic case. When B is not orthogonal the isospectral sets are cylin
drical real analytic submanifolds of L(R)(2) ([0, 1])(2) X SL(2, R), a
nd their sections for fixed boundary conditions are real analytic subm
anifolds of L(R)(2) ([0, 1])(2).