A New Discrete Integrable System Derived from a Generalized Ablowitz-Ladik Hierarchy and Its Darboux Transformation | Zendy

Xianbin Wu | Zendy; Weiguo Rui | Zendy; Xiaochun Hong | Zendy

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A New Discrete Integrable System Derived from a Generalized Ablowitz-Ladik Hierarchy and Its Darboux Transformation

Author(s) -

Xianbin Wu,

Weiguo Rui,

Xiaochun Hong

Publication year - 2012

Publication title -

discrete dynamics in nature and society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.264

H-Index - 39

eISSN - 1607-887X

pISSN - 1026-0226

DOI - 10.1155/2012/652076

Subject(s) - integrable system , transformation (genetics) , darboux integral , hierarchy , mathematics , soliton , pure mathematics , algebra over a field , physics , nonlinear system , quantum mechanics , geometry , chemistry , biochemistry , curvature , economics , market economy , gene

We find an interesting phenomenon that the discrete system appearing in a reference can be reduced to the old integrable system given by Merola, Ragnisco, and Tu in another reference. Differing from the works appearing in the above two references, a new discrete integrable system is obtained by the generalized Ablowitz-Ladik hierarchy; the Darboux transformation of this new discrete integrable system is established further. As applications of this Darboux transformation, different kinds of exact solutions of this new system are explicitly given. Investigatingthe properties of these exact solutions, we find that these exact solutions are not pure soliton solutions, but their dynamic characteristics are very interesting

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