S I ] 1 3 A ug 2 01 4 On W 1 + ∞ 3-algebra and integrable system
S I ] 1 3 A ug 2 01 4 On W 1 + ∞ 3-algebra and integrable system
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发表时间：
2014
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通讯作者：
Min-Ru Chen;Shi-kun Wang;Xiao-Li Wang;Ke Wu;Wei-zhong Zhao
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作者：
Min-Ru Chen;Shi-kun Wang;Xiao-Li Wang;Ke Wu;Wei-zhong Zhao
构造了无限维W1+∞ 3-代数，并研究了它与可积系统的关系.由于在算子Nambu 3-括号中具有固定生成元W 00的W1+∞ 3-代数恢复了W1+∞代数，因此从Nambu-Poisson发展方程导出KP族是很自然的.对于W1+∞ 3-代数的一般情形，我们直接从Nambu-Poisson发展方程导出了具有不同哈密顿量对的KP和KdV方程.我们还讨论了W1 +∞ 3-代数与无色散KdV方程之间的联系。由于Nambu-Poisson演化方程包含两个哈密顿量，揭示了KP族哈密顿量对之间的深层联系。进而给出了W1+∞ 3-代数在复玻色域上的一种实现.基于复玻色场的Nambu 3-括号，导出了（广义）非线性薛定谔方程，并给出了它在光孤子中的应用。
We construct the W1+∞ 3-algebra and investigate the relation between this infinitedimensional 3-algebra and the integrable systems. Since the W1+∞ 3-algebra with a fixed generator W 0 0 in the operator Nambu 3-bracket recovers the W1+∞ algebra, it is natural to derive the KP hierarchy from the Nambu-Poisson evolution equation. For the general case of the W1+∞ 3-algebra, we directly derive the KP and KdV equations from the Nambu-Poisson evolution equation with the different Hamiltonian pairs. We also discuss the connection between theW1+∞ 3-algebra and the dispersionless KdV equations. Due to the Nambu-Poisson evolution equation involves two Hamiltonians, the deep relationship between the Hamiltonian pairs of KP hierarchy is revealed. Furthermore we give a realization of W1+∞ 3-algebra in terms of a complex bosonic field. Based on the Nambu 3-brackets of the complex bosonic field, we derive the (generalized) nonlinear Schrödinger equation and give an application in optical soliton.