$w_{\infty}$ 3-algebra and integrable system

Details $w_{\infty}$ 3-algebra and integrable system $w_{\infty}$ 3-algebra and integrable system

2012-01-02

arxiv.org/abs/1201.0417v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

4 pages

Scientific paper

We investigate the relation between the $w_{\infty}$ 3-algebra and dispersionless KdV hierarchy. The $w_{\infty}$ 3-algebra can be expressed as the Nambu-Poisson bracket structure of the Fourier transform field. The dispersionless KdV hierarchy for the corresponding Fourier transform field follows from the Nambu-Poisson evolution equation given the suitable Hamiltonians. We find that these Hamiltonians are in involution for the Poisson and Nambu-Poisson bracket structures, respectively. Due to the Nambu-Poisson evolution equation involving two Hamiltonians, the more intriguing relationships between these Hamiltonians are revealed.

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