Abstract
Reference [1] presented a gauge transformation between thex parts of the AKNS eigenvalue problem and those of the JM (Jaulent-Miodek) eigenvalue problem. In this paper we discuss the correspondence between thet parts of the AKNS eigenvalue problem and thet parts of the JM eigenvalue prohlem 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.
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References
Zhang Etang, Chen Dengyuan, Zheng Yunbo, Zhu Guochen, Li Yishen, A Class of Normal Transformation of the Eigenvalue Problems,Journal of China University of Science and Technology,13 (1983), Math. Issue, 54–62.
Li Yishen, Gu Xinshen, Zou Maorong, Three Kinds of Darboux Transformation for the Evolution Equations which Connect with AKNS Eigenvalue Problem,Acta Mathematica Sinica (New Series),32 (1987), 143–151.
Li Yishen, Zhuang Dawei, Nonlinear Evolution Equations Associated with Eigenvalue Problems of Energy Dependent Potentials,Acta Mathematica Sinica,254 (1982), 464–474.
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Project supported by the Science Fund of the Ministry of Education.
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Zhang, Y., Gu, X. A correspondence between the AKNS hierarchy and the JM hierarchy. Acta Mathematicae Applicatae Sinica 4, 307–315 (1988). https://doi.org/10.1007/BF02007234
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DOI: https://doi.org/10.1007/BF02007234