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<p>In this work, we focus on the higher-order Chen-Lee-Liu equation, which is a higher-order form of the derivative Schrödinger equation. We present the action-angle variables of the higher-order Chen-Lee-Liu equation by the inverse scattering method. First, the higher-order Chen-Lee-Liu equation is derived from the variational principle and given in Hamiltonian form. Then, the Poisson brackets between the scattering data of the higher-order Chen-Lee-Liu equation were successfully determined by introducing the matrix tensor product. Interestingly, we relate the coordinate expressions to the spectral parameter expressions of Hamiltonian for the higher-order Chen-Lee-Liu equation with the help of conservation laws.</p>

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Poisson structure and action-angle variables for the higher-order Chen-Lee-Liu equation

  • 期刊论文

  • 发表日期：

    2025年4月10日

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  • Yun-Zhi Gao,
  • Shou-Fu Tian

摘要

In this work, we focus on the higher-order Chen-Lee-Liu equation, which is a higher-order form of the derivative Schrödinger equation. We present the action-angle variables of the higher-order Chen-Lee-Liu equation by the inverse scattering method. First, the higher-order Chen-Lee-Liu equation is derived from the variational principle and given in Hamiltonian form. Then, the Poisson brackets between the scattering data of the higher-order Chen-Lee-Liu equation were successfully determined by introducing the matrix tensor product. Interestingly, we relate the coordinate expressions to the spectral parameter expressions of Hamiltonian for the higher-order Chen-Lee-Liu equation with the help of conservation laws.