### 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 |
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Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Publication status | Published - 2002 |

### Publication series

Name | Memorandum |
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Publisher | Department of Applied Mathematics, University of Twente |

No. | 1615 |

ISSN (Print) | 0169-2690 |

### Keywords

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

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## Cite this

Kersten, P. H. M., & Sorin, A. S. (2002).

*Bi-Hamiltonian structure of the $N=2$ supersymmetric $\alpha = 1$ KdV hierarchy*. (Memorandum; No. 1615). Enschede: University of Twente, Department of Applied Mathematics.