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

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  • Hongxia Wu
  • Liangjuan Gao
  • Jingxin Liu
  • Yunbo Zeng

Abstract

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.

Suggested Citation

  • Hongxia Wu & Liangjuan Gao & Jingxin Liu & Yunbo Zeng, 2016. "Two Kinds of Darboux-Bäcklund Transformations for the -Deformed KdV Hierarchy with Self-Consistent Sources," Advances in Mathematical Physics, Hindawi, vol. 2016, pages 1-11, September.
    • Handle: RePEc:hin:jnlamp:8153752
    DOI: 10.1155/2016/8153752
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