Li, Zhu; Dong, Huanhe Integrable couplings of the multi-component Dirac hierarchy and its Hamiltonian structure. (English) Zbl 1221.37130 Chaos Solitons Fractals 36, No. 2, 290-295 (2008). The authors obtain multi-component integrable couplings of the Dirac hierarchy by using the vector loop algebra \(\widetilde G_M\). Then, according to the quadratic-form identity, the Hamiltonian structure of the above system is presented. Reviewer: Messoud A. Efendiev (Berlin) Cited in 6 Documents MSC: 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) Keywords:multi-component Dirac hierarchy; Hamiltonian structure; loop algebra PDF BibTeX XML Cite \textit{Z. Li} and \textit{H. Dong}, Chaos Solitons Fractals 36, No. 2, 290--295 (2008; Zbl 1221.37130) Full Text: DOI References: [1] Tu, Guizhang, J math phys, 30, 2, 330-338, (1989) [2] Ma, Wenxiu, Chinese J contemp math, 13, 1, 79-89, (1992) [3] Fan, Engui, J math phys, 41, 11, 7769, (2000) [4] Zhang, Dajun; Chen, Dengyuan, J phys A: math gen, 35, 7225, (2002) [5] Zhang, Yufeng; Yan, Qingyou, Chaos, soliton & fractals, 16, 263, (2003) [6] Zhang, Yufeng, Phys lett A, 317, 3, 280-286, (2003) · Zbl 1027.37042 [7] Zhang, Yufeng, Acta Mathematica sinica, 1, 141, (2005) [8] Zhang, Yufeng; Zhang, Hongqing, J math phys, 43, 466-473, (2002) [9] Guo, Fukui; Zhang, Yufeng, Chaos, soliton & fractals, 19, 5, 1207-1216, (2004) [10] Guo, Fukui; Zhang, Yufeng, J math phys, 44, 12, 5793-5803, (2003) [11] Zhang, Yufeng, Chaos, soliton & fractals, 27, 555-559, (2002) [12] Zhang, Yufeng, Phys lett A, 327, 438-441, (2004) [13] Zhang, Yufeng, Chaos, soliton & fractals, 21, 305-310, (2004) [14] Xia, Tiecheng, Chaos, soliton & fractals, 23, 1163-1167, (2005) [15] Zhang, Yufeng; Tam, Honwah, Chaos, soliton & fractals, 23, 651-655, (2005) [16] Dong, Huanhe; Zhang, Ning, Commun theor phys, 44, 6, 997-1001, (2005) [17] Xia, Tiecheng; You, Fucai, Chaos, soliton & fractals, 26, 606-613, (2005) [18] Guo, Fukui; Zhang, Yufeng, J phys A: math gen, 38, 8537-8548, (2005) [19] Qiao, Zhijun, Chinese quart J math, 12, 1, 1-3, (1997) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.