Letters in Mathematical Physics

, Volume 49, Issue 1, pp 33–45 | Cite as

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

  • Ming-Hsien Tu
  • Jiin-Chang Shaw
  • Chin-Rong Lee


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

KdV hierarchy q-deformations Darboux–Bäcklund transformations 


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Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Ming-Hsien Tu
    • 1
  • Jiin-Chang Shaw
    • 2
  • Chin-Rong Lee
    • 3
  1. 1.Department of MathematicsNational Chung Cheng UniversityMinhsiung, ChiayiTaiwan
  2. 2.Department of Applied MathematicsNational Chiao Tung UniversityHsinchuTaiwan
  3. 3.Department of PhysicsNational Chung Cheng UniversityMinhsiung, ChiayiTaiwan

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