A differential-difference hierarchy associated with relativistic Toda and Volterra hierarchies

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)4578-4585
Journal / PublicationPhysics Letters, Section A: General, Atomic and Solid State Physics
Issue number25
Publication statusPublished - 16 Jun 2008


By embedding a free function into a compatible zero curvature equation, we enlarge the original differential-difference hierarchy into a new hierarchy with the free function which still admits zero curvature representation. The new hierarchy not only includes the original hierarchy, but also the well-known relativistic Toda hierarchy and the Volterra hierarchy as special reductions by properly choosing the free function. Infinitely many conservation laws and Darboux transformation for a representative differential-difference system are constructed based on its Lax representation. The exact solutions follow by applying the Darboux transformation. © 2008 Elsevier B.V. All rights reserved.

Research Area(s)

  • Conservation law, Darboux transformation, Differential-difference hierarchy, Hamiltonian structure, Relativistic Toda hierarchy, Volterra hierarchy