In this paper, we give a procedure of how to discretize the recursion
operators by considering unified bilinear forms of integrable hierarchies. As
two illustrative examples, the unified bilinear forms of the AKNS hierarchy and
the KdV hierarchy are presented from their recursion operators. Via the
compatibility between soliton equations and their auto-B\"acklund
transformations, the bilinear integrable hierarchies are discretized and the
discrete recursion operators are obtained. The discrete recursion operators
converge to the original continuous forms after a standard limit.Comment: 11Page

Hu, Xingbiao

Yu, Guofu

Zhang, Yingnan

English

arXiv

In this paper, we give a procedure for discretizing recursion operators byutilizing unified bilinear forms within integrable hierarchies. To illustratethis approach, we present unified bilinear forms for both the AKNS hierarchyand the KdV hierarchy, derived from their respective recursion operators.Leveraging the inherent connection between soliton equations and theirauto-B\"acklund transformations, we discretize the bilinear integrablehierarchies and derive discrete recursion operators. These discrete recursionoperators exhibit convergence towards the original continuous forms whensubjected to a standard limiting process.Comment: 16Page

Episciences.org

Integrable discretization of recursion operators and unified bilinear forms to soliton hierarchies

arXiv.org e-Print Archive

Integrable discretization of recursion operators and unified bilinear
  forms to soliton hierarchies

In this paper, we give a procedure for discretizing recursion operators by
utilizing unified bilinear forms within integrable hierarchies. To illustrate
this approach, we present unified bilinear forms for both the AKNS hierarchy
and the KdV hierarchy, derived from their respective recursion operators.
Leveraging the inherent connection between soliton equations and their
auto-B\"acklund transformations, we discretize the bilinear integrable
hierarchies and derive discrete recursion operators. These discrete recursion
operators exhibit convergence towards the original continuous forms when
subjected to a standard limiting process

Xingbiao Hu

Guofu Yu

Yingnan Zhang

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Integrable discretization of recursion operators and unified bilinear forms to soliton hierarchies

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arXiv.org e-Print Archive

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