Generalized Bäcklund-Darboux transformation (GBDT): conservation laws, rational extensions and bispectrality

Abstract

Bäcklund-Darboux transformations are closely related to the integrability and symmetry problems. For the generalized Bäcklund-Darboux transformation (GBDT), we consider conservation laws, rational extensions and bispectrality. We use the case of the nonlinear optics equation (and its auxiliary linear system) as an example.