# Bi-Hamiltonian structure of the $N=2$ supersymmetric $\alpha = 1$ KdV hierarchy

P.H.M. Kersten, A.S. Sorin

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## Abstract

The $N=2$ supersymmetric ${\alpha}=1$ KdV hierarchy in $N=2$ superspace is considered and its rich symmetry structure is uncovered. New nonpolynomial and nonlocal, bosonic and fermionic symmetries and Hamiltonians, bi-Hamiltonian structure as well as a recursion operator connecting all symmetries and Hamiltonian structures of the $N=2$ ${\alpha}=1$ KdV hierarchy are constructed in explicit form. It is observed that the algebra of symmetries of the $N=2$ supersymmetric ${\alpha}=1$ KdV hierarchy possesses two different subalgebras of $N=2$ supersymmetry.
Original language English Enschede University of Twente, Department of Applied Mathematics Published - 2002

### Publication series

Name Memorandum Department of Applied Mathematics, University of Twente 1615 0169-2690

• MSC-35Q51
• MSC-35Q53
• IR-65802
• EWI-3435
• MSC-35Q58