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A Block Matrix Loop Algebra and Bi-Integrable Couplings of the Dirac Equations

Published online by Cambridge University Press:  28 May 2015

Wen-Xiu Ma ,
Huiqun Zhang  and
Jinghan Meng
Wen-Xiu Ma*
Affiliation:
Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA
Huiqun Zhang*
Affiliation:
Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA College of Mathematical Science, Qingdao University, Qingdao, Shandong 266071, P.R. China
Jinghan Meng*
Affiliation:
Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA
*
Corresponding author. Email Address: mawx@cas.usf.edu
Corresponding author. Email Address: zhanghuiqun@qdu.edu.cn
Corresponding author. Email Address: jmeng@mail.usf.edu
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Abstract

A non-semisimple matrix loop algebra is presented, and a class of zero curvature equations over this loop algebra is used to generate bi-integrable couplings. An illustrative example is made for the Dirac soliton hierarchy. Associated variational identities yield bi-Hamiltonian structures of the resulting bi-integrable couplings, such that the hierarchy of bi-integrable couplings possesses infinitely many commuting symmetries and conserved functionals.

Keywords

37K0537K1035Q53Integrable couplingmatrix loop algebraHamiltonian structure

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Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 3 , Issue 3 , August 2013 , pp. 171 - 189
Copyright
Copyright © Global-Science Press 2013

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