Lax-integrable Laberge–Mathieu hierarchy of supersymmetric nonlinear dynamical systems and its finite-dimensional reduction of Neumann type

  • O. E. Hentosh

A compatibly bi-Hamiltonian Laberge–Mathieu hierarchy of supersymmetric nonlinear dynamical systems is obtained by using a relation for the Casimir functionals of the central extension of a Lie algebra of superconformal even vector fields of two anticommuting variables. Its matrix Lax representation is determined by using the property of the gradient of the supertrace of the monodromy supermatrix for the corresponding matrix spectral problem. For a supersymmetric Laberge–Mathieu hierarchy, we develop a method for reduction to a nonlocal finite-dimensional invariant subspace of the Neumann type. We prove the existence of a canonical even supersymplectic structure on this subspace and the Lax–Liouville integrability of the reduced commuting vector fields generated by the hierarchy.


Vries Equation Laurent Series Neumann Type Coadjoint Action Liouville Integrability 
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Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  • O. E. Hentosh
    • 1
  1. 1.Institute of Applied Problems of Mechanics and MathematicsUkrainian National Academy of SciencesLvivUkraine

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