A correspondence between AKNS hierarchy and the JM hierarchy (Q1114868)

\textit{E. Zhang}, \textit{D. Chen}, \textit{Y. Zheng}, \textit{G. Zhu} and \textit{Y. Li} [A class of normal transformation of the eigenvalue problems, J. China Univ. Sci. Tech. 13, Math. Issue, 54-62 (1983)] presented a gauge transformation between the x parts of the AKNS eigenvalue problem and those of the JM (Jaulent-Miodek) eigenvalue problem. In this paper we discuss the correspondence between the t parts of the AKNS eigenvalue problem and the t parts of the JM eigenvalue problem under the gauge transformation, and give a correspondence between the AKNS hierarchy and the JM hierarchy and also three types of Darboux transformation for the JM hierarchy.