Hamiltonian Structures and Integrability of Frobenius Algebra-Valued (n, m)th KdV Hierarchy. Issue 3 (3rd July 2017)

• Record Type: Journal Article
• Authors: Zhang, Hai
• Is Part Of: Journal of nonlinear mathematical physics. Volume 24:Issue 3(2017)
• Page Start: 315
• Page End: 327
• Publication Date: 2017-07-03
• Subjects: ℱ-valued (n, m)th KdV hierarchy -- Hamiltonian structure -- hereditary recursion operator -- flow equation; 37K10 -- 35Q53; Nonlinear theories -- Periodicals; Mathematical physics -- Periodicals; 515.252
• DOI: 10.1080/14029251.2017.1341695
• Languages: English
• ISSNs: 1402-9251

Abstract

Abstract : We introduce Frobenius algebra ℱ -valued ( n, m ) th KdV hierarchy and construct its bi-Hamiltonian structures by employing ℱ -valued pseudo-differential operators. As an illustrative example, the (1, 1) th -valued case is analyzed in detail. Its Hamiltonian structures and recursion operator are derived. Infinitely many symmetries, conservation laws and explicit flow equations are also obtained.