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On Darboux–Bäcklund Transformations for the Q-Deformed Korteweg–de Vries Hierarchy |
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| Authors: | Tu Ming-Hsien Shaw Jiin-Chang Lee Chin-Rong |
| Institution: | (1) Department of Mathematics, National Chung Cheng University, Minhsiung, Chiayi, 621, Taiwan;(2) Department of Applied Mathematics, National Chiao Tung University, Hsinchu, 300, Taiwan;(3) Department of Physics, National Chung Cheng University, Minhsiung, Chiayi, 621, Taiwan |
| Abstract: | 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. |
| Keywords: | KdV hierarchy q-deformations Darboux– Bä cklund transformations |
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