The complex Hamiltonian systems with real‐valued Hamiltonians are generalized to deduce quasi‐periodic solutions for a hierarchy of derivative nonlinear Schrödinger (DNLS) equations. The DNLS hierarchy is decomposed into a family of complex finite‐dimensional Hamiltonian systems by separating the temporal and spatial variables, and the complex Hamiltonian systems are then proved to be integrable in the Liouville sense. Due to the commutability of complex Hamiltonian flows, the relationship between the DNLS equations and the complex Hamiltonian systems is specified via the Bargmann map. The Abel‐Jacobi variable is elaborated to straighten out the DNLS flows as linear superpositions on the Jacobi variety of an invariant Riemann surface. Finally, by using the technique of Riemann‐Jacobi inversion, some quasi‐periodic solutions are obtained for the DNLS equations in view of the Riemann theorem and the trace formulas.

中文翻译：

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导数非线性Schrödinger方程中的复杂Hamilton系统和拟周期解

将具有实值哈密顿量的复杂哈密顿量系统广义化，以推导非线性非线性薛定ding（DNLS）方程层次的准周期解。通过分离时间和空间变量，将DNLS层次结构分解为一系列复杂的有限维哈密顿系统，然后证明复杂的哈密顿系统在Liouville意义上是可积的。由于复杂哈密顿流的可交换性，DNLS方程和复杂哈密顿系统之间的关系通过Bargmann映射指定。精心设计了Abel-Jacobi变量，以理顺DNLS流作为不变Riemann曲面的Jacobi变体上的线性叠加。最后，通过使用黎曼-雅各比反演技术，