Does the supersymmetric integrability imply the integrability of Bosonic sector

Journal Article · Mon Mar 08 00:00:00 EST 2010 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.3367239· OSTI ID:21371057

Popowicz, Ziemowit ^[1]

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1. Institute of Theoretical Physics, University of Wroclaw, pl. M. Borna 50-205 Wroclaw (Poland)

The answer is no. This is demonstrated for two equations that belong to the supersymmetric Manin-Radul N = 1 Kadomtsev-Petviashvili (MRSKP) hierarchy. The first one is the N = 1 supersymmetric Sawada-Kotera equation recently considered by Tian and Liu. We define the bi-Hamiltonian structure for this equation which however does not reduce in the bosonic limit to the known bi-Hamiltonian structure. The second equation is obtained from the Lax operator of the fifth order in the supersymmetric derivatives which in the bosonic sector reduces to the system of interacted two KdV equations discovered by Drinfeld and Sokolov in 1981 and later rediscovered by Sakovich and Foursov.

• OSTI ID: 21371057
• Journal Information: AIP Conference Proceedings, Vol. 1212, Issue 1; Conference: 1. international workshop on nonlinear and modern mathematical physics, Beijing (China), 15-21 Jul 2009; Other Information: DOI: 10.1063/1.3367239; (c) 2010 American Institute of Physics; ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
HAMILTONIANS
INTEGRAL EQUATIONS
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LAX THEOREM
MATHEMATICAL OPERATORS
SUPERSYMMETRY
DIFFERENTIAL EQUATIONS
EQUATIONS
PARTIAL DIFFERENTIAL EQUATIONS
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