This article is cited in 9 papers

Lax Integrable Supersymmetric Hierarchies on Extented Phase Spaces

Oksana Ye. Hentosh

IInstitute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, 3B Naukova Str., Lviv, 79060, Ukraine

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.

Keywords: Lax type flows; “ghost” symmetries; the Davey–Stewartson system.

MSC: 35Q53; 35Q58; 37K10; 37K30; 37K35; 58A50

Received: October 27, 2005; in final form December 21, 2005; Published online January 4, 2006

Language: English

DOI: 10.3842/SIGMA.2006.001

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ArXiv: nlin.SI/0601007