## Darboux
Transformation and Soliton-like Solutions for a Generalized q-KdV Hierarchy
ע⣺ՓJournal of the
Physical Society of JapanVol. 73, No. 11, November, 2004, pp. 2991C2995l
ʹՈעՓĳ̎
Engui FANF
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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