Positive and Negative Integrable Hierarchies: Bi-Hamiltonian Structure and Darboux–Bäcklund Transformation
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-12-30
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
Two integrable hierarchies are derived from a novel discrete matrix spectral problem by discrete zero curvature equations.
They correspond, respectively, to positive power and negative power expansions of Lax operators with respect to the spectral parameter.
The bi-Hamiltonian structures of obtained hierarchies are established by a pair of Hamiltonian operators through discrete trace identity.
The Liouville integrability of the obtained hierarchies is proved.
Through a gauge transformation of the Lax pair, a Darboux–Bäcklund transformation is constructed for the first nonlinear different-difference equation in the negative hierarchy.
Ultimately, applying the obtained Darboux–Bäcklund transformation, two exact solutions are given by means of mathematical software.
American Psychological Association (APA)
Zhang, Ning& Xu, Xi-Xiang. 2020. Positive and Negative Integrable Hierarchies: Bi-Hamiltonian Structure and Darboux–Bäcklund Transformation. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-15.
https://search.emarefa.net/detail/BIM-1195890
Modern Language Association (MLA)
Zhang, Ning& Xu, Xi-Xiang. Positive and Negative Integrable Hierarchies: Bi-Hamiltonian Structure and Darboux–Bäcklund Transformation. Mathematical Problems in Engineering No. 2020 (2020), pp.1-15.
https://search.emarefa.net/detail/BIM-1195890
American Medical Association (AMA)
Zhang, Ning& Xu, Xi-Xiang. Positive and Negative Integrable Hierarchies: Bi-Hamiltonian Structure and Darboux–Bäcklund Transformation. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-15.
https://search.emarefa.net/detail/BIM-1195890
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1195890