Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 6 (2010), 018, 10 pages      arXiv:0910.2389
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

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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