Two Kinds of Darboux-Bäcklund Transformations for theq-Deformed KdV Hierarchy with Self-Consistent Sources
Keyword(s):
Two kinds of Darboux-Bäcklund transformations (DBTs) are constructed for theq-deformedNth KdV hierarchy with self-consistent sources (q-NKdVHSCS) by using theq-deformed pseudodifferential operators. Note that one of the DBTs provides a nonauto Bäcklund transformation for twoq-deformedNth KdV equations with self-consistent sources (q-NKdVESCS) with different degree. In addition, the soliton solution to the first nontrivial equation ofq-KdVHSCS is also obtained.