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Darboux Transformation and Soliton-like Solutions for a Generalized q-KdV Hierarchy

注意：本论文已在Journal of the Physical Society of Japan，Vol. 73, No. 11, November, 2004, pp. 2991–2995发表
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Engui FAN（范恩贵）
Institute of Mathematics and Key Lab for Nonlinear Mathematical Models and Methods,
Fudan University, Shanghai 200433, P. R. China
(Received July 5, 2004)

Abstract:By introducing a q-deformed spectral problem, we derive a new generalized q-KdV hierarchy with variable coefficients. Darboux matrix technique is further extended to construct an explicit and universal Darboux transformation for the q-KdV hierarchy. It is found that the Darboux transformation admits a theorem of permutability theorem and a superposition formula. In particular, the soliton-like solutions whose speeds may depend on time variable t are obtained by applying the Darboux transformation and superposition formula.
KEYWORDS: generalized q-KdV hierarchy, Darboux transformation, theorem of permutability, soliton-like solution
DOI: 10.1143/JPSJ.73.2991

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