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

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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