Darboux and binary Darboux transformations for the nonautonomous discrete KP equation

Abstract

It is shown how Darboux and binary Darboux transformations for a nonautonomous discrete KP equation can be obtained from fermion analysis. This equation is obtained by considering a generalized Miwa transformation; it is also shown to be linked to the discrete KP equation by a special gauge transformation. The Darboux and binary Darboux transformations are used to discuss general classes of solutions in the form of Casorati- and Gramm-type determinants. N-soliton solutions are discussed as well.