An integrable coupling hierarchy of Dirac integrable hierarchy, its Liouville integrability and Darboux transformation
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Authors
Xi-Xiang Xu
- College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China.
Ye-Peng Sun
- School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan, 250014, China.
Abstract
An integrable coupling hierarchy of Dirac integrable hierarchy is presented by means of zero curvature representation.
A Hamiltonian operator involving two parameters is introduced, and it is used to derive a pair of Hamiltonian operators.
A bi-Hamiltonian structure of the obtained integrable coupling hierarchy is constructed with the aid of Magri pattern of bi-
Hamiltonian formulation. Moreover, we prove the Liouville integrability of the obtained integrable coupling hierarchy and
establish a Darboux transformation of the integrable coupling. As an application, an exact solution of the integrable coupling of
Dirac equation is given.
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ISRP Style
Xi-Xiang Xu, Ye-Peng Sun, An integrable coupling hierarchy of Dirac integrable hierarchy, its Liouville integrability and Darboux transformation, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 6, 3328--3343
AMA Style
Xu Xi-Xiang, Sun Ye-Peng, An integrable coupling hierarchy of Dirac integrable hierarchy, its Liouville integrability and Darboux transformation. J. Nonlinear Sci. Appl. (2017); 10(6):3328--3343
Chicago/Turabian Style
Xu, Xi-Xiang, Sun, Ye-Peng. "An integrable coupling hierarchy of Dirac integrable hierarchy, its Liouville integrability and Darboux transformation." Journal of Nonlinear Sciences and Applications, 10, no. 6 (2017): 3328--3343
Keywords
- Dirac integrable hierarchy
- integrable coupling
- Hamiltonian operator
- Magri pattern
- bi-Hamiltonian structure
- Darboux transformation.
MSC
References
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