Bargmann type finite-dimensional reductions of the Lax integrable supersymmetric Boussinesq hierarchy and their integrability - Hentosh, O.E. (Нелінійні коливання, 2015)
For the supersymmetric Boussinesq hierarchy, related with the Lax type flows on the space dual to the Lie algebra of superintegro-differential operators of one anticommuting variable for some non-self-adjoint superdifferential operator, the method of the Bargmann type finite-dimensional reductions is developed. We prove existence of an even exact supersymplectic structure on the corresponding invariant finite-dimensional supersubspace of the supersymmetric Boussinesq hierarchy as well as the Lax – Liouville integrability of commuting vector fields, generated by the hierarchy and reduced to this supersubspace.