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

B. K. Chung·K. G. Joo·Soonkeon Nam
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Abstract

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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B. K. Chung, K. G. Joo, Soonkeon Nam. 1993-03-30. Classical $W_3^{(2)}$ algebra and its Miura map. https://arxiv.org/abs/hep-th/9303165

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