The extended $Z_N$-Toda hierarchy

Abstract

The extended flow equations of a new $Z_N$-Toda hierarchy which takes values in a commutative subalgebra $Z_N$ of $gl(N,\mathbb{C})$ is constructed. Meanwhile we give the Hirota bilinear equations and tau function of this new extended $Z_N$-Toda hierarchy(EZTH). Because of logarithm 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 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 Sato theory.

22 Pages, Theoretical and Mathematical Physics, 185(2015), 1614-1635

References in corpus (6)

• Rogue waves of the Hirota and the Maxwell-Bloch equations
• The Extended Bigraded Toda hierarchy
• Block type symmetry of bigraded Toda Hierarchy
• Dispersionless bigraded Toda Hierarchy and its additional symmetry
• Solutions of bigraded Toda hierarchy
• Hirota equations for the extended bigraded Toda hierarchy and the total descendent potential of CP^1 orbifolds

Cited by in corpus (9)

• Gauge transformation and symmetries of the commutative multi-component BKP hierarchy
• Quantum torus symmetries of multicomponent modified KP hierarchy and reductions
• Bäcklund transformations of $Z_n$-Sine-Gordon systems
• 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
• Extensions of the finite nonperiodic Toda lattices with indefinite metrics
• A strongly coupled extended Toda hierarchy and its Virasoro symmetry
• BiHom-Lie brackets and the Toda equation