A strongly coupled extended Toda hierarchy and its Virasoro symmetry

Abstract

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.

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

References in corpus (4)

• The Extended Bigraded Toda hierarchy
• Solutions of bigraded Toda hierarchy
• On the extended multi-component Toda hierarchy
• Simple Lax Description of the ILW Hierarchy