By means of reduction expression with solutions of constant-coefficient nonlinear Schrödinger system, analytical partially nonlocal ring-like spatiotemporal superimposed second-order Akhmediev and Ma breather solution is derived from the Darboux approach. In or coordinate, the cylindrical multilayer structure of Akhmediev and Ma breathers is embedded in the center, and rings of Akhmediev breather and plane of Ma breather extend out. Moreover, the influence of the radius and thickness parameters is studied. The Hermite parameter has impact on the layer structure of ring-like superimposed second-order breather in the direction.

中文翻译：

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谐波势下部分非局域环状时空叠加二阶呼吸器

通过常系数非线性薛定谔系统解的约简表达，从达布方法中推导出部分非局域环状时空叠加二阶Akhmediev和Ma Breather解的解析解。在或坐标系中，Akhmediev和Ma呼吸器的圆柱形多层结构嵌入中心，Akhmediev呼吸器的环和Ma呼吸器的平面向外延伸。此外，还研究了半径和厚度参数的影响。Hermite参数对环形叠加二阶通气层在方向上的层结构有影响。