Hamiltonian structures of generalized Manin–Radul super-KdV and constrained super KP hierarchies

Abstract

A study of Hamiltonian structures associated with supersymmetric Lax operators is presented. Following a constructive approach, the Hamiltonian structures of Inami-Kanno super KdV hierarchy and constrained modified super KP hierarchy are investigated from the reduced supersymmetric GelfandDickey brackets. By applying a gauge transformation on the Hamiltonian structures associated with these two nonstandard super Lax hierarchies, we obtain the Hamiltonian structures of generalized Manin-Radul super KdV and constrained super KP hierarchies. We also work out a few examples and compare them with the known results.

Binary nonlinearization of the super AKNS system under an implicit symmetry constraint

“…and verify that they are also integrals of motion of the constrained spatial system (10) and temporal system (19). Making use of (22), it is easy to find that (23) are in involution in pair.…”

“…The constrained (6N+4)-dimensioanl systems (10) and (19) are super Hamiltonian systems, whose 3N+2 integrals of motion (24) are in involution in pair and functionally independent over supersymmetry manifold R 4N +2|2N +2 .…”

“…Such as Darboux transformation [15,16], Hamiltonian structures [17,18,19], and so on. In very recent years, nonlinearization of the super AKNS system has been studied in Ref.…”

Nonlinear Super Integrable Couplings of Super Classical Boussinesq Hierarchy

“…Zhang [16] once employed two kinds of explicit Lie algebra F and G to obtain the nonlinear integrable couplings of the GJ hierarchy and Yang hierarchy, respectively. It is easy to see that Lie algebra F given in [16] is isomorphic to the Lie algebra span 1 2 3 4 5 6 { , , , , , } e e e e e e in gl (6,2). So we can obtain nonlinear integrable couplings of super GJ and Yang hierarchy easily.…”

Nonlinear Super Integrable Couplings of Super C-KdV Hierarchy

“…Zhang [19] once employed two kinds of explicit Lie algebra F and G to obtain the nonlinear integrable couplings of the GJ hierarchy and Yang hierarchy, respectively. It is easy to see that Lie algebra F given in [19] is isomorphic to the Lie algebra span 1 2 3 4 5 6 { , , , , , } e e e e e e in gl (6,2). So we can obtain nonlinear integrable couplings of super GJ and Yang hierarchy easily.…”