Virasoro symmetry algebra of Dirac soliton hierarchy

Abstract

A hierarchy of first-degree time-dependent symmetries is proposed for Dirac soliton hierarchy and their commutator relations with time-dependent symmetries are exhibited. Meantime, a hereditary structure of Dirac soliton hierarchy is elucidated and a Lax operator algebra associated with Virasoro symmetry algebra is given.

A New Super Extension of Dirac Hierarchy

“…The super integrable system (17) may admit nonlinearization. Moreover, the super Dirac system (17) may inherit various other integrable characteristics, such as first-degree time-dependent symmetries [13] and Bä cklund transformation [14]. In particular, it is of interest to study multi-integrable couplings and the corresponding super Hamiltonian structures of the super Dirac system (17) by the super variational identity [15].…”

Algebraic-geometric solutions of the Dirac hierarchy

“…Обратные задачи для системы Дирака в различных условиях обсуждались в работах [1]- [5]. Проведены исследования алгебры симметрии Вирасоро иерархии Дирака [6]. N -кратное преобразование Дарбу и солитонные решения для нелинейной системы Дирака были получены в работе [7].…”

A subalgebra of Lie algebra A2 and its associated two types of loop algebras, as well as Hamiltonian structures of integrable hierarchy

“…Also, we obtain the integrable coupling of the above hierarchy according to the definition of integrable coupling and its constructing method. [15][16][17][18][19][20][21][22] Furthermore, we directly generalized the Lie algebra A n−1 = sl͑n , C͒ and presented new Lie algebra A n−1 ‫ء‬ = gl͑n , C͒.…”