A strongly coupled extended Toda hierarchy and its Virasoro symmetry

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.
Comment: 16 Pages. arXiv admin note: text overlap with arXiv:1410.3657, arXiv:1504.06125, arXiv:1403.0684