Bi-Hamiltonian structure of the extended noncommutative Toda hierarchy. Issue 3 (2nd July 2016)

• Record Type: Journal Article
• Authors: Li, Chuanzhong; Song, Tao
• Is Part Of: Journal of nonlinear mathematical physics. Volume 23:Issue 3(2016)
• Page Start: 368
• Page End: 382
• Publication Date: 2016-07-02
• Subjects: noncommutative Toda hierarchy -- extended noncommutative Toda hierarchy -- bi-Hamiltonian structure; 37K05 -- 37K10 -- 37K40; Nonlinear theories -- Periodicals; Mathematical physics -- Periodicals; 515.252
• DOI: 10.1080/14029251.2016.1199498
• Languages: English
• ISSNs: 1402-9251

Abstract

Abstract : The noncommutative Toda hierarchy is studied with the help of Moyal deformation by a reduction on the non-commutative two dimensional Toda hierarchy. Further we generalize the noncommutative Toda hierarchy to the extended noncommutative Toda hierarchy. To survey on its integrability, we construct the bi-Hamiltonian structure and noncommutative conserved densities of the extended noncommutative Toda hierarchy by means of the R-matrix formalism. This extended noncommutative Toda hierarchy can be reduced to the extended multicomponent Toda hierarchy, extended ZN -Toda hierarchy, extended Toda hierarchy respectively by reductions on Lie algebras.