Two Kinds of Darboux-Bäcklund Transformations for the q-Deformed KdV Hierarchy with Self-Consistent Sources

Abstract

Two kinds of Darboux-Bäcklund transformations (DBTs) are constructed for the q-deformed Nth KdV hierarchy with self-consistent sources (q-NKdVHSCS) by using the q-deformed pseudodifferential operators. Note that one of the DBTs provides a nonauto Bäcklund transformation for two q-deformed Nth KdV equations with self-consistent sources (q-NKdVESCS) with different degree. In addition, the soliton solution to the first nontrivial equation of q-KdVHSCS is also obtained