PARAMETERS OF DARBOUX TRANSFORMATION FOR REDUCED AKNS, KAUP-NEWELL AND PCF SYSTEMS

FOr the integrable system with u(p, q) reduction, there is a well-known sufficient conditionto choose the parameters: the spectral parameters only take two mutually conjugate valuesand the solutions of the Lax pair should satisfy certain orthogonal relations. In this paper, theauthor proves that, for the AKNS system, the Kaup-Newed system and the principal chiralfield (PCF), this condition is also necessary for generic potentials with the u(p, q) reduction.FOr some other reductions, sufficiency and necessity of more constraints are proved.