Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 2 (2006), 001, 11 pages     nlin.SI/0601007      https://doi.org/10.3842/SIGMA.2006.001

Lax Integrable Supersymmetric Hierarchies on Extended Phase Spaces

Oksana Ye. Hentosh
Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, 3B Naukova Str., Lviv, 79060 Ukraine

Received October 27, 2005, in final form December 21, 2005; Published online January 04, 2006

Abstract
We obtain via Bäcklund transformation the Hamiltonian representation for a Lax type nonlinear dynamical system hierarchy on a dual space to the Lie algebra of super-integral-differential operators of one anticommuting variable, extended by evolutions of the corresponding spectral problem eigenfunctions and adjoint eigenfunctions, as well as for the hierarchies of their additional symmetries. The relation of these hierarchies with the integrable by Lax (2|1+1)-dimensional supersymmetric Davey-Stewartson system is investigated.

Key words: Lax type flows; "ghost" symmetries; the Davey-Stewartson system.

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