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

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

Research output: Book/ReportReportOther research output

### 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

hierarchies
symmetry
supersymmetry
algebra
operators

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

### 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.
Kersten, P.H.M. ; Sorin, A.S. / Bi-Hamiltonian structure of the $N=2$ supersymmetric $\alpha = 1$ KdV hierarchy. Enschede : University of Twente, Department of Applied Mathematics, 2002. (Memorandum; 1615).
@book{5c98fde13bef4ff6a0eb7bb9eb1c96c9,
title = "Bi-Hamiltonian structure of the $N=2$ supersymmetric $\alpha = 1$ KdV hierarchy",
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.",
keywords = "MSC-35Q51, MSC-35Q53, IR-65802, EWI-3435, MSC-35Q58",
author = "P.H.M. Kersten and A.S. Sorin",
note = "Imported from MEMORANDA",
year = "2002",
language = "English",
series = "Memorandum",
publisher = "University of Twente, Department of Applied Mathematics",
number = "1615",

}

Kersten, PHM & Sorin, AS 2002, Bi-Hamiltonian structure of the $N=2$ supersymmetric $\alpha = 1$ KdV hierarchy. Memorandum, no. 1615, University of Twente, Department of Applied Mathematics, Enschede.

Bi-Hamiltonian structure of the $N=2$ supersymmetric $\alpha = 1$ KdV hierarchy. / Kersten, P.H.M.; Sorin, A.S.

Enschede : University of Twente, Department of Applied Mathematics, 2002. (Memorandum; No. 1615).

Research output: Book/ReportReportOther research output

TY - BOOK

T1 - Bi-Hamiltonian structure of the $N=2$ supersymmetric $\alpha = 1$ KdV hierarchy

AU - Kersten, P.H.M.

AU - Sorin, A.S.

N1 - Imported from MEMORANDA

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

KW - MSC-35Q51

KW - MSC-35Q53

KW - IR-65802

KW - EWI-3435

KW - MSC-35Q58

M3 - Report

T3 - Memorandum

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

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -

Kersten PHM, Sorin AS. Bi-Hamiltonian structure of the $N=2$ supersymmetric $\alpha = 1$ KdV hierarchy. Enschede: University of Twente, Department of Applied Mathematics, 2002. (Memorandum; 1615).