Classical $W_3^{(2)}$ algebra and its Miura map

Details Classical $W_3^{(2)}$ algebra and its Miura map Classical $W_3^{(2)}$ algebra and its Miura map

1993-03-30

arxiv.org/abs/hep-th/9303165v1

J.Korean Phys.Soc.26:557-561,1993

Physics

High Energy Physics

High Energy Physics - Theory

12pages, KHTP-93-02, SNUCTP-93-17

Scientific paper

We verify that the fractional KdV equation is a bi-hamiltonian system using the zero curvature equation in $SL(3)$ matrix valued Lax pair representation, and explicitly find the closed form for the hamiltonian operators of the system. The second hamiltonian operator is the classical version of the $W^{(2)}_3$ algebra. We also construct systematically the Miura map of $W^{(2)}_3$ algebra using a gauge transformation of the $SL(3)$ matrix valued Lax operator in a particular gauge, and construct the modified fractional KdV equaiotn as hamiltonian system.

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