On the extended multi-component Toda hierarchy

Abstract

The extended flow equations of the multi-component Toda hierarchy are constructed. We give the Hirota bilinear equations and tau function of this new extended multi-component Toda hierarchy(EMTH). Because of logarithmic terms, some extended vertex operators are constructed in generalized Hirota bilinear equations which might be useful in topological field theory and Gromov-Witten theory. Meanwhile the Darboux transformation and bi-Hamiltonian structure of this hierarchy are given. From the Hamiltonian tau symmetry, we give another different tau function of this hierarchy with some unknown mysterious connections with the one defined from the point of wave functions.

29 Pages, to appear in Mathematical Physics, Analysis and Geometry. arXiv admin note: substantial text overlap with arXiv:1403.0684

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• Rogue waves of the Hirota and the Maxwell-Bloch equations
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• Tau function and Hirota bilinear equations for the Extended bigraded Toda Hierarchy
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• Solutions of bigraded Toda hierarchy
• The multicomponent 2D Toda hierarchy: Discrete flows and string equations
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• Hirota equations for the extended bigraded Toda hierarchy and the total descendent potential of CP^1 orbifolds

Cited by in corpus (8)

• Gauge transformation and symmetries of the commutative multi-component BKP hierarchy
• Quantum torus symmetries of multicomponent modified KP hierarchy and reductions
• Sato theory on the $q$-Toda hierarchy and its extension
• Dispersionless and multicomponent BKP hierarchies with quantum torus symmetries
• Virasoro symmetry of the constrained multi-component KP hierarchy and its integrable discretization
• Quantum torus algebras and B(C) type Toda systems
• A strongly coupled extended Toda hierarchy and its Virasoro symmetry
• Inner Product in Highest-Weight Representation