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SIGMA 6 (2010), 018, 10 pages arXiv:0910.2389
https://doi.org/10.3842/SIGMA.2010.018
Contribution to the Proceedings of the XVIIIth International Colloquium on Integrable Systems and Quantum Symmetries
The Integrability of New Two-Component KdV Equation
Ziemowit Popowicz
Institute for Theoretical Physics, University of Wroclaw, Wroclaw 50204, Poland
Received October 19, 2009, in final form February 04, 2010; Published online February 12, 2010
Abstract
We consider the bi-Hamiltonian representation of the
two-component coupled KdV equations discovered by
Drinfel'd and Sokolov and rediscovered by Sakovich and Foursov.
Connection of this equation with the supersymmetric
Kadomtsev-Petviashvilli-Radul-Manin hierarchy is presented. For
this new supersymmetric equation the Lax representation and odd
Hamiltonian structure is given.
Key words:
KdV equation; Lax representation; integrability; supersymmetry.
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