THE FERMIONIC APPROACH TO DARBOUX TRANSFORMATIONS

Starting from the free fermion description of the one-component KP hie rarchy, we establish a connection between this approach and the theory of Darboux and binary Darboux transformations. Certain difference ide ntities-allowing for the treatment of both continuous as well as discr ete evolution equations-turn out to be crucial: first to show that any solution of the associated (adjoint) linear problems can always be ex pressed as a superposition of KP (adjoint) wavefunctions and then to i nterpret Darboux (and binary Darboux) transformations as Backlund tran sformations in the fermion language.