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Advances in Mathematical Physics
Volume 2016, Article ID 8153752, 11 pages
Research Article

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

1Department of Mathematics, School of Sciences, Jimei University, Xiamen 361021, China
2Department of Mathematics, The University of Texas Rio Grande Valley, Edinburg, TX 78539, USA
3Department of Mathematics, Tsinghua University, Beijing 100084, China

Received 19 April 2016; Accepted 23 July 2016

Academic Editor: Pavel Kurasov

Copyright © 2016 Hongxia Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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