In this letter, we derive the isospectral and nonisospectral soliton hierarchies of a higher-order Zakharov–Shabat spectral problem where nonlinear Schrödinger equation and modified KdV equation are included. Furthermore, it is discussed that the new integrable properties are found about the higher-order Zakharov–Shabat hierarchy, including the master symmetry and the time dependent symmetry.

中文翻译：

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高阶Zakharov-Shabat层次结构的可积性

在这封信中，我们导出了包含非线性Schrödinger方程和修正KdV方程的高阶Zakharov-Shabat光谱问题的等光谱和非等光谱孤子层次。此外，还讨论了有关高阶Zakharov-Shabat层次结构的新可积性，包括主对称性和与时间有关的对称性。