A differential-difference hierarchy associated with relativistic Toda and Volterra hierarchies |
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Authors: | Engui Fan Huihui Dai |
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Institution: | a School of Mathematical Science, Fudan University, Shanghai 200433, PR China b Department of Mathematics, University of Missouri-Columbia, Columbia, Missouri, MO 65211, USA c Department of Mathematics, City University of Hong Kong, Hong Kong SAR, PR China |
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Abstract: | 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. |
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Keywords: | 02 30 lk 05 50 +q 04 20 Jb |
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