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\(W_{1+\infty}3\)-algebra and the higher-order nonlinear Schrödinger equations in optical fiber. (English) Zbl 07263838
Summary: In terms of \(W_{1+\infty}3\)-algebra, the generalized Nambu-Poisson evolution equations involving two Hamiltonians are constructed. Given the different Hamiltonian pairs, the higher-order nonlinear Schrödinger equations are obtained. Meanwhile, on the basis of the Maxwell equations, the higher-order nonlinear Schrödinger equations in optical fiber are derived in detail. Furthermore, the relations between the higher-order nonlinear Schrödinger equations in optical fiber and the higher-order nonlinear Schrödinger equations based on the \(W_{1+\infty}3\)-algebra are investigated. The bright soliton, dark soliton and the periodic traveling wave solutions of the higher-order nonlinear Schrödinger equation based on the \(W_{1+\infty}3\)-algebra are also derived.
MSC:
00 General and overarching topics; collections
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