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

1998/11/06 by Ming-Hsien Tu, Jiin-Chang Shaw, Chin-Rong Lee
Physics and Astronomy · #solv-int #nlin.SI

paper · pdf

published as Lett. Math. Phys., 49(1): 33-45, July 1999 · 12 pages, Revtex, no figures

arxiv created 1998/11/06 · arxiv updated 2009/11/30

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.

Related

• Q-deformed KP hierarchy: Its additional symmetries and infinitesimal Bäcklund transformations
• Geometric Bäcklund--Darboux transformations for the KP hierarchy
• Revisiting Bäcklund-Darboux transformations for KP and BKP integrable hierarchies
• Algebra of Deformed Differential Operators and Induced Integrable Toda Field Theory
• Darboux Transformations from Reductions of the KP Hierarchy