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Volume 3, Issue 3
A Block Matrix Loop Algebra and Bi-Integrable Couplings of the Dirac Equations

Wen-Xiu Ma, Huiqun Zhang & Jinghan Meng

DOI: 10.4208/eajam.250613.260713a

East Asian J. Appl. Math., 3 (2013), pp. 171-189.

Published online: 2018-02

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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

Integrable coupling, matrix loop algebra, Hamiltonian structure.

  • AMS Subject Headings

37K05, 37K10, 35Q53

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-3-171, author = {Wen-Xiu Ma, Huiqun Zhang and Jinghan Meng}, title = {A Block Matrix Loop Algebra and Bi-Integrable Couplings of the Dirac Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {3}, number = {3}, pages = {171--189}, 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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.250613.260713a}, url = {http://global-sci.org/intro/article_detail/eajam/10854.html} }
TY - JOUR T1 - A Block Matrix Loop Algebra and Bi-Integrable Couplings of the Dirac Equations AU - Wen-Xiu Ma, Huiqun Zhang & Jinghan Meng JO - East Asian Journal on Applied Mathematics VL - 3 SP - 171 EP - 189 PY - 2018 DA - 2018/02 SN - 3 DO - http://doi.org/10.4208/eajam.250613.260713a UR - https://global-sci.org/intro/article_detail/eajam/10854.html KW - Integrable coupling, matrix loop algebra, Hamiltonian structure. AB -

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.

Wen-Xiu Ma, Huiqun Zhang and Jinghan Meng. (2018). A Block Matrix Loop Algebra and Bi-Integrable Couplings of the Dirac Equations. East Asian Journal on Applied Mathematics. 3 (3). 171-189. doi:10.4208/eajam.250613.260713a
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