A Strongly Coupled Extended Toda Hierarchy and its Virasoro Symmetry

  • Chuanzhong LiEmail author


As a generalization of the integrable extended Toda hierarchy and a reduction of the extended multicomponent Toda hierarchy, from the point of a commutative subalgebra of \(gl(2,\mathbb {C})\), we construct a strongly coupled extended Toda hierarchy(SCETH) which will be proved to possess a Virasoro type additional symmetry by acting on its tau-function. Further we give the multi-fold Darboux transformations of the strongly coupled extended Toda hierarchy.


Strongly coupled extended Toda hierarchy Additional symmetry Virasoro Lie algebra 

Mathematics Subject Classifications (2010)

37K05 37K10 37K20 



This work is funded by the National Natural Science Foundation of China under Grant No. 11571192, and K. C. Wong Magna Fund in Ningbo University.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsNingbo UniversityNingboPeople’s Republic of China

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