On Darboux-Bäcklund Transformations for the Q-Deformed Korteweg-de Vries Hierarchy

Abstract

We study Darboux-Bäcklund transformations (DBTs) for the $q$-deformed Korteweg-de Vries hierarchy by using the $q$-deformed pseudodifferential operators. We identify the elementary DBTs which are triggered by the gauge operators constructed from the (adjoint) wave functions of the hierarchy. Iterating these elementary DBTs we obtain not only $q$-deformed Wronskian-type but also binary-type representations of the tau-function to the hierarchy.

12 pages, Revtex, no figures

Cited by in corpus (5)

• The gauge transformation of the constrained semi-discrete KP hierarchy
• The compatibility of additional symmetry and gauge transformations for the constrained discrete Kadomtsev-Petviashvili hierarchy
• The determinant representation of the gauge transformation for the discrete KP hierarchy
• The applications of the gauge transformation for the BKP hierarchy
• The integral type gauge transformation and the additional symmetry for the constrained KP hierarchy